Game theory Flashcards
Define one shot game, finitely repeated game and infinitely repeated game + zero sum
-one shot is played once.
-finitely repeated game is a game in which is played over a fixed number of times/iterations.
-Infinitely repeated game refers to game in which is played an uncertain number of times, however there is a chance that the game ends after each round.
-zero sum game : players gain is equal to loss for other person: chess, checkers etc. Payoffs can be maximised by backward induction. Most games are not Zero sum.
Define
-imperfect and perfect information
-incomplete and complete information
-asymmetric information
-Imperfect infomration refers tot when a player/s do not know all of the previous moves of an other player/s. Perfect: a player/s knows all the previous moves of all opponents.
-Incomplete information refers to when a player/s are not fully aware of other players’ preferences, strategies, or payoffs, leading to uncertainty. Complete: fully aware.
-Asymmetric information occurs when an information gap between players occurs. Players may have more/less information than others, AI can be in-perfect or incomplete.
define nash equiblirum
-Refers to when each players strategy is optimal given the strategies of all other players, everyone is doing the best they can given the opponents decisions.
-A situation in which no player has incentive to deviate strategies, to improve payoff, based on the opponents strategy.
-When players are both best responding in simultaneous game.
steps to calculate roll back equiblirum + format for writing it (path)
-refers to starting at the end nodes and working back to determine optimal strategy taking into account actions of players.
- Start at last decision nodes, identify optimal choices for that player making the decision.
- Backtrack to previous decision nodes, applying the same logic at each point, by anticipating the optimal choice of the player in the future (previous node). Until reach beginning.
- conclude rollback equblirum strategies and corresponding payoffs.
The path taken from the terminal nodes to the root, first node, is known as the rollback equilibrium
Describe forward and backward induction + how to write the roll back in an answer
-Forward induction refers to observing past behaviour of other platers to make predictions on future moves. Observing previous actions, players can infer other players beliefs, intentions, strategies etc and make more informed decisions in future.
-Begin at the start of the game and reason forward. eg) poker, gaining information by thinking about the past/past events)
-Backward induction refers to starting at the end of the game and working backwards to determine optimal decisions. Refers to anticipating reactions to a decision made.
-WHEN writing answers, rollback equilbirum is the final payoff and strategies, path is strategy path.
calculating number of strategies in a decision tree, each decision has same number of actions, different number of actionss
-Each node has same number of actions/decisions:
S = (number of decisions/actions available at each node(branches))^num of decision nodes.
eg)5 decision nodes, 2 branches/actions at each = 32 strategies.
-Nodes may have different number of actions/decisions:
S = product of number of choices/brances at each individual node.
Eg) 1
Node1 = 3actions, N2 = 2, Node3 = 2, 12 strats.
Define deciison problem and strategic interaction
-Decision problem refers to a decision by a player that is not influenced by decisions/strats of others. Based on rationality and utility of decisions/outcomes. Example picking fruits, items for PRIVATE consumption.
-Strategic interaction refers to an interaction where a players payoffs/utility and outcomes depend on not only what you do but other people. Eg) pen kick, bidding in auction, apple or blackberry.
Descrive first and second mover advantage
-F mover advantage allows the player to carry out their preffered strategy, to gain strategic position, coordinate? etc. eg) Patents
-S mover advantage allows the player moving to adapt their strategy to the choices of other players, first mover cannot do this. Can learn from the first movers actions, avoid mistakes etc (innovation)
Eg) sequential zero sum games, use perfect information to respond optimally.
rollback equilibrium with indifferences + ask gpt for example+ harder examples
-Same process as finding normal rollback, but when a player is indifferent just see what player before will do for either decision.
-Multiple. equilbira may exist.
Eg) player 2 indifferent between UP or down, see what player 1 will do IF player 2 chooses up and same for down.
Difference between discrete and continous strategies in simulatenous games
- IN simultaneous games, discrete strategies involve a limited set of choices,
-while continuous strategies offer an infinite range of options.
Define strategy profile
-refers to a combination of strategies chosen by all players in a game, where each player’s strategy is specified for every possible situation in the game.
Describe strictly dominant and weakly strategiees
-Strategy X strictly dominates strategy Y if, regardless of what other playres do, X generates a strictly higher payoff than Y. u(x,Z) > u(Y,Z) for all possible Z (stategy profiles of other players)
-Strategy X weakly dominates strategy Y, if regardless of what other players do, X generates a higher OR THE SAME PAYOFF. u(x,Z) >= u(Y,Z) for all possible Z (stategy profiles of other players)
Define iterated elimination of strictly dominated strategies IESDS (to find rationais)
IESDS is a method used to simplify analysis of games by eliminating strategies that a rational player would never choose.
-THIS PROCESS helps narrow down the possible outcomes of a game by removing “bad” strategies until only the best (or more rational) ones are left.
-Process that determines rationisable strategies
Process of IESDS + define what it means for a game to be dominance solvable
Process:
1.For each player remove all strictly dominated strategies (stategies that are strictly dominated not strictly dominant)
2. now check if any additional strategies have become strictly dominated, if so remove them.
3. Repeat this process until NO strategies are eliminated (NEVER ELIMINATE WEAKLY DOMINATED STATS ONLY STRICTLY)
Define a pure coordination game
-Refers to a game in which players have identical prefernces, main goal is to coordinate on the same strategy to maximise payoffs for both.
-No conflict of interest within the game, outcome is optiaml when players choose the same action
-In pure coordation games there is a single strategy pair which players achieve the best possbile pauoff, and equilbirum occurs when players coordinate on this strategy.
Define a coordination game
-A game in which players benefit from alligning their strategies or making the same choices.
-Players may face challenges in coordinating their actions to achieve a mutually desirable outcome. In other words, players win or do well when they manage to coordinate their strategies effectively
define focal points in coordination games + what makes it focal
-Focal points refer to strategies players tend to choose without communication as they STAND OUT as the obvious choice that everyone expects others to choose aswell.
-allows players to cooridnate on a common strategy.
-focal equilibriumrefers to an outcome in a coordination game that players are likely to choose because it stands out as the most obvious option.
-Factors such as salience, uniqueness, predictable, cultural norms make outcomes focal, (players coordinate and choose these outcomes without communation), obvious option
define games with pareto ranked equilbiria + eg + deine pareto effeiicnt equiblrium
-Games in which nash equilibria can be ranked according to their Pareto efficiency, meaning that some equilibria make all players better off than others.
-Eg) coordination games such as stagg hunt, min effort and critical mass
-PE equlrium , an outcome in which no playter can be made better off by making someone else worse off.
define payoff and risk dominant equilbirum + eg
-A payoff-dominant equilibrium is the outcome that provides the highest total payoff to all players, making it the most socially optimal choice. Stag Stag outcome.
-A risk-dominant equilibrium is the outcome that minimizes individual risk, even if it provides a lower total payoff compared to the payoff-dominant equilibrium. Eg) choosing to hunt hare
define pre play communication (one way and two way) in coordination game + why done
-Pre play, communication before the game has started. (can be one or two way)
-One way involves one player being able to communicate information/signal to other player, they cant respond. Can ignore/take onboard (assymtery)
-Two way, noth players can communiacte/signal informtion back and forth, share intentions and coordiate on optimal strategies. Can establish trust and reduce uncertainty.
-To ensure best possible payoffs for both players by coordinating and alligning strategies
define inefficient lock in + reason why it occurs
-refers to a situation where players become stuck in an equilibrium that is suboptimal/inefficient, even though better outcomes are possible.
-Refers to coordination to an ineffienct/suboptimal eequiblrium.
-Typically occurs because each player individually has no individual incentive to deviate from the current situation, even though a collective move by all players to a specific strategy would benefit everyone.
Methods of Preventing/overcoming inefficinet lock in
-establish trust
-pre play communication
-introduce incentives/punishment for choosing optimal strategies for the group/choosing ineffieint ones.
-Repetition, players learn over greater itertions to coordinate to the more optimal outcome.
define a continous strategy in game theory + eg
-A strategy in which any player can pick a value/strategy wihtin a continous range, rather than from a discrete set of options/strategies. Potentially infinite amount of strategies.
-Bertrand and cournot oligpoly, choosing prices and q from a continous range eg) 0- 1000.
Define Bertrand oligopoly and Cournot oligopoly and how to find equiblrium in all cases
-Cournot oligpoly refers to price compeition between firms. In simultenous games equiblrium occurs when the best response functions intersect. In sequential, rollback equibirlum is used to find how the first player will set prices based on best response of the second player (p1 anticipates p2 is best responding.)
-Cournot oligpoly refers to quanitiy compeition between firms.
Describe nash equiblirum in the bertrand olipolgy with PERFECT substitues. + what if different marigainl costs + why cant undercut in equiblrium
-Goods are identical in nature and we assume the seller with lower price will ‘capture’ all customers.
-Nash equilibrium occurs when all firms set their p= marginal cost, as any deviation by a firm (charging a higher price) would result in losing all customers to competitors
-The firm with the lower MC will undercut the other firms price/cost by a infiently small amount and take all customers. Cant undercut in nash equiblrium as already driven down to MC –> would make negative
-find profit functions for each case (p1>p2, p1< p2, p1=p2) and BRF and see what scenarios lead to profit/best responses
In a cournot oligpoly, q competition, fomula for equiblrium quanitiy, price and BRF’s
-N > 1 people in market
-C is marginal cost
-common price given by inverse demand curve
-q* = a -c / n + 1
-p* = a - n(a-c) / n+1
-assumong slope of inverse demand curve b is 1. a - sum of all quantities (Q)
Define rationalizable strategy + how to find
- is a strategy that can be a best response for a belief about the other players’ strategies, assuming rationality.
-takes into account
-Follow the rationisibilty or IESDS process, any strategies that survive are rationaisable, however with IESDS doesnt consider beleifs.
Process of determining the nash equiblirum (simultanous games) in a game table + ask gpt to gen a question to practice + 3 players example
-For each player determine best responses for the other players strategy. When players are both best responding, NE. Cells in which both players playing their best responses. MARK CELLS WHEN PLAYERS ARE BEST RESPONDING, then when both marks then NE
-Can also just go through each individal cell and determine if any player has an incentive to devidate, therefore not/is NE.
Determining dominant strategies (simultanous game) in a game table process + ask GPT for an example to find dominant strategies
- compare the payoffs for each strategy of a player under all possible strategies of the other player(s); a strategy is dominant if it always gives a higher payoff, no matter which strategy the other player chooses.
(-For each player see what strategy is better for each strategy of the other player)
example for player 1) if p2 selects X what does they prefeer, if p2 selects Y what do they prefer, if the same strat, dom etc.
- Repeat this process for all players.
-Recall: strictly dominant strategy always gives a higher payoff than any other strategy, while a weakly dominant strategy gives a payoff at least as good as others and strictly better in at least one case.
Ask gpt for example of working through the IESDS
-step by step compare strategiues for players eg) a vs b, c vs b and remove if strictly dominated.
define what it means for a game to be dominance solveable
-dominance solvable if repeatedly removing strictly dominated strategies leaves just one outome, one strat for each player.
Define the rationisaibilty process + differnce to IESDS + get example for gpt
Identify each player’s best responses: , determine the strategies that are the best response to some belief about what the other players will do.
Eliminate non-best responses: Remove any strategies that are not the best response to any possible belief about the other players’ strategies.
Repeat until no more strategies can be eliminated:
- involves eliminating strategies that are not best responses to any possible belief about the other players’ actions. Repeat until no more non best responses can be eliminated
-Both result in rationisable strategies survign
define what the IESDS and rationsibilty processes lead to
IESDS leads to a set of strategies that are not strictly dominated,
Rationalizability leads to a set of strategies that can be the best response to some belief about the other player’s strategy.
IESDS surviving strategies are those that cannot be strictly dominated by any strategy, meaning they are never worse than another strategy in all scneario
Rationalizability: surviving strategies are those that can be the best response to some belief about the other player’s strategies, assuming both players are rational.
Define assumptions of the location game (conflict game) + player profits + nash equilbirum + best responses
-Two sellers, each sellers selling at seperate location (in between 0-100 for example). Each buyer will buy to closest seller.
-Profit player 1 is x + y / 2, midpoint of the 2 players locations. Player 2 profit = 1 - player 1 profit.
-Nash equiblirum when both players are located in the middle, midpoint of all locations, eg) x = y = 50.
-If opponent is at a lcoation greater thna midpoint (eg) y > 50) locate slightly to left, Xr = y - 1.
-If opponent is location less than midpoint (eg) y < 50) locate slightly to right of opponent. Xr = y + 1. Same foes for player 2.
Exaplin why in location game (conflict game) the extremes locations eg x=0 and y=100 are unstable. + eg)
-Icentive to deviate for both players to capture more of the market instead of half. Eg) Profit x=0y=100 50 each, where as x=5 y=100 profit player 1 = 52.5
-This instability forces players to devidate inwards to maxmise profits and this converges to the nash of in the middle for both sellers.
-The extremes are optimal for the buyers, each buyer is closest to one of the sellers, minimises buyer travel costs
Explain assumptions expected payoffs/proftis in the rent seeking game (conflict game)
-N players competing for prize V by making investments xi. Prob win the prize for a player is respective investment over sum of investments (or 1/n if no investments made.)
-Expected payoff for player 1: = xi / sum other playres investmetns * V -xi
Explain best responses + interpret and nash equilbirum in rent seeking game (conflict game) + formula for equiblrium investment x*
-Best response function is the derivative of profit function in respect to xi (investment). given by:
Xri = sqrt(V*sum of all other players investments) - sum of all other players investments
-Initially as sum of other playres investments grows, best response investment increases, however as it grows further competition becomes to fierce –> fall in best response investment. Demonstrating diminishing returns.
-Nash occurs when all players are best responding (BRF’s intersect), or when all playes are investing the same amount (x1=x2=x3) (symmetric equiblerium) If n = 2, nash equiblrium investment given by: v/4.
-outcome typically inefficient, players invest excessively to gain prize (sum of investments > V)
-x* = v(n-1) /n^2 –> when n = 2 x*= v/4
Define assumptions and profits in the travellers dilema game (conflict game)
-Bag lost travveliing, airline can reinburse value but they dont know the true value. You and another player must make a claim, within a range (eg)80-200). If claims are equal full value reinbursed, if different person with lower valuation gets reinbursed and player with higher pays a penalty of V to other player.
-profits for player i given by:
π(ci,cj)= cj- V if ci > cj
π(ci,cj)= ci + V if ci < cj
π(ci,cj)= ci = cj if ci=cj
Explain best responses and nash equiblirum in the travellers dilema game (conflict game) + results
-BR depends on other players valuation.
-If other players valuation, cj, is equal to the minimmum valuation possible (eg 80) BR to value at this lowest possible amount, 80. ci= cj if cj = lowest possible value, 80.
-If other players valuation, cj, is greater than the minimum possible value, BR is to value ci one unit lower than thier valuation (ci = cj -1 if cj > min value/80) to max profit and receive penalty.
-NE occurs when both players value, ci= cj at the minium amount possible eg) 80. No incentive to deviate. (min valuation possible, min valuation possible) (80,80)
-experiment show undercutting more likely at higher penalties, more risk to value higher with bigger V.
Explain the assumptions, best response and nash equilbirum in the beauty contest game (conflict game)
-assume N number of players picks a number between a range (eg 0-100). Winner is the player closest to 2/3rds of the average number chosen. X
-Best response, which takes into account antipation, is to pick 2/3rd of the anticipated average X. BR depends on expected average/choice of other players.
-If guesses are integers and N is large two NE:
When everyone chooses 0, average is 0 no incentive to deviate, 2/3rd would be 0.
When everyone chooses 1, average = 1 therefore 2/3 of average is closer to 1 than 0, no incentive to deviate to 0.
Define normative and descriptuve interpretation of NE
Normative Iinterpretation involveshow rational players should behave, assuming they aim to maximize their utility and assume rationality.
Descriptive Interpretation involves how players actually behave in strategic interactions/games, behaviour is different from NE predictions.
3 points on why player behaviour/outcomes differ from the NE
1.NE assumes, most of the time, that people are expected to be selfish utility maximisers, however this assumption can be improved by modelling preferences. Players may care about other social factors, altruism, social norms etc.
2.NE assumes people have unlimited cognitive abilities and arent sensitive to incentives, this can be replaced by modelling mistakes or the learning process.
3.NE assumes people have correct beliefs, assumes players correctly predict what others will do.can be relaxed by modelling uncertain beleifs/mistakes.
When does behaviour typically converge to the NE
-Repeated interactions enable learning and belief formation.
-partner matching can lead to collusion.
-Simplfying games or allocating tools to help with calculating best responses.
-When players receive feedback based on past payoff information, most games converge to NE.
Two main methods of moddelling learning within games
define mixed strategies and pure strategy
-A mixed strategy is when a player doesn’t pick just one action, from a set of trategies, but instead chooses between actions/strategies based on probability.
-A pure strategy refers to when a player picks a specific strategy with certaininty from a set of strategies
Define a prisoners dilema game and solutions + example of PD + dominant stategy in PD
- game where two players can either cooperate or defect, NE is when both oplayers defect. Game in which the socially optmium outcome is not the NE.
-defection offers a higher individual payoff at the expense of the other, leading to the temptation to defect even though mutual cooperation would be better for both.
-Dom strat is to defect, no matter what opponent does.
eg) business pricing, C: collude, D: undercut and make more than other.
SOlutions:
-Infnite repetition
-Changing payoffs
-Communication
-Introducing punishments and rewards
define inequality aversion
-Inequialty aversion refers to behaviour by individuals that avoids situations in which there are unfair outcomes or distribution of resources/benefits.
Define TFT strategy and gt strats (repeated games/cooepration) + how they encourage cooperation/optimal outcome (C,C in PD)
-The Grim Trigger involves cooperating until the opponent defects once. If the opponent defects, the player then “triggers” a permanent strategy of defection (i.e., they defect for the rest of the game).
–Tit for tat strategy refers to cooperating in the first round then from here mimicking the behaviour of the other player. So if the opponent cooperates, the TFT player cooperates in the next round; if the opponent defects, the TFT player defects in the next round.
- strategies rely on fact players care about the future and are willing to cooperate over time, as repeated interactions allow them to encourage cooperation and discourage defection.
-These strategies encourage/reward cooperation and punish defection. more effective in repeated games
Formula for number of strategies in n round reperated game, assume 2 avaliable actuons per round
The number of strategies in an
n-round repeated game = 2^(2^n)
Nash E or rollback in a one shot and twice repeated PD game + finetyl repeateed PD game
One-Shot : Nash equilibrium is for both players to defect because defection is the best response to the other player’s defection or cooperation
Twice-Repeated Prisoner’s Dilemma: Using backward induction, the Nash equilibrium is for both players to defect in both rounds because defection is the dominant strategy in both rounds, with no future punishment or reward. Essentialyl two one shot games
In a finitely repeated PD, Nash equilibrium is both to defect in each round, rollback shows that defection is the dominant strategy in the last round, and this behavior carries over to previous rounds due to the lack of future punishment
what does the best strategyin an infitnely played prisoners dilemma depend on
depend on the discount factor, which represents how much players value future payoffs compared to immediate ones.
- A higher discount factor might encourage more cooperation, as players are more willing to maintain long-term gains.
-, a lower discount factor might lead to more defection, as short-term benefits. Thus, the optimal strategy could shift based on how much players discount future rewards.
benefits of TFT
Clear, simple and recognisable to other strategies
-Nice ‘socially nice’ - begins with cooperation
-Provocable: immediate retaliation from other players deflection
-Forgiving: immediately returns to c if opponent returns to c
Describe equilbirum, which involves strategies such as TFT and GT, in infintely repeated prisoner dilema games
the equilibrium typically involves strategies like Tit for Tat or Grim Trigger. As is DESCRIBED BY THE STRATEGIES EACH PLAYER Plays + why they have no inentive to deviate. Weigh up payoffs of strategies for both players and see if incentive to deviate/indifference point.
With TFT, cooperation is sustained/no incentive to deviate if players value future gains enough to be deterred by potential retaliation. If the discount factor is high the strategy is more likely to support cooperation long trm. If the discount factor is low, players may prioritize short-term gains and defect more often.
For the Grim Trigger strategy, the discount factor is important. The threat of permanent punishment for a single defection only works if the future consequences (the loss of cooperation) are significant enough to outweigh the short-term benefit of defection. If discount high, concerned about long term payoffs, may not retaliate, permenant lower payoffs than mutual cooepratiom.
Solving these games (METHOD OF FINDING NE in games with multiple stages/subgames eg) PD then punishment stage + ask gpt to explain an example walkrotugh of process with game table for each stage.
To solve games with multiple stages and subgames:
Start at final stage/subgame and find NE, then work backward through each stage, substituting the NE payoffs from previous stages into earlier ones. Repeat this process until you reach the first stage, and the resulting strategy profile is the Subgame Perfect Equilibrium (SPE), where no player has an incentive to deviate at any stage.
-If multiple NE exist at any stage, repeat the process and rollback for each nash equilibrium to determine all possible Subgame Perfect Equilibria (SPE).
-To write nash write all optinaml strategies at each stage with respective payoffs.
Define a collective action game + eg games
-collective action game is a situation/game where individuals or players must decide whether and how much to contribute to a shared goal or collective good/project, often in the presence of conflicting incentives.
eg)PGG, critical mass, proffession choice, neibhourhood game. These games are also conflict, cooperation, coordination etx.
Define critical mass game
is a game in which a player’s payoffs depends whether players adopt a behavior that becomes beneficial only if enough participants (the critical mass) do the same, below which participation yields low or negative payoffs and above which it becomes beneficial
Describe nash equilbirum in critical mass game + what is the payoff dom equiblria + why the critical mass isnt a nash + indifference point and best responses for contibuting
-Everryone contributes
-Nobody contributes.
-Indiffernce point is when payoff from contributing = payoff from not. To find when contributing is the best response when payoff from contributing > not.
-“Critical mass is typically not a Nash equilibrium because it is unstable with a finite number of players (but becomes more stable with infinite players, as individual decisions have less influence).
-A small deviation from the critical mass can tip the system and lead it to converge to one of the extremes.
-For example, if the critical mass is exceeded, the payoff from contributing increases with more contributors, incentivizing others to join, leading to full contribution.
Eg) if the critical mass is not met, the payoff for contributing becomes lower than not contributing, making it optimal for players to not contribute, which converges to zero contribution.”
-Everyone contributing is typically the payoff dominant equiblrium, offers higher payoffs for everyone.
define when a socially optomum outcome occurs + eg
socially optimal outcome is one where the total payoffs of all players are maximized, often referred to as the social welfare. It represents the situation where the collective benefit to society is at its highest, even if individual incentives don’t always align.
-Maxmise total game payoffs
-PD multiple players, profession game
define unconditional and conditional strategic moves
A conditional move is a contingent decision that depends on the actions of the other players. The player commits to a specific action only if certain conditions are met.
-An unconditional move is a commitment to a specific course of action, regardless of what the other players do. The player makes this move to influence the other players’ decisions in their favor/improve payoffs.
Two types of commitment
Unconditional and conditional.
-Restricting freedom commitment, commitment by making it impossible to change action once committed, eg) removing steering wheel from driving game. Imoprotant that other player knows about this type of commitment.
-Changing payoffs commitment make alterations to personal payoffs such that the best possible outcome becomes dominant. EG) giving money to a third party which wont be returned unless you carry out the commitment. Also public promises, damage reputation etc. Anything that will negatively impact payoff if best outcome isnt carried out, D. Making commitment more attractive using these outside factors.
Factors to consider when making a threat.
-Comminication, will opp cut off/ignore, missinformation?
-Negotiations, depending on motivation off opp preventing negotiations may improve payoff, eg) terrrorists..
-Credible.
-Size of threat, threats to small/large may be ineffective, proportional to severity of opponents actions.
-Need to be able to be carried out, prevent reputational damage. Current reputation may also impact effectivness.
-Understanding the rationality of opponent, to know which threats may work or not.
-Threats that hurt opponent personally to make sure they work.
-Brinkmanship, escalating a situation to brink of crisis to pressure oppoent into ‘giving in’ to threat and alterning decision.
-Whether opponent is using salami tactics, and whether need to avoid them. (soluyion: threaten to carry out smaller proportinal threats to the smaller ‘lines crossed’/salami slice actions.)
Methods in which can make a threat/promises more credible (impove chance of better payoff/influencing oppoenents decision)
-Automating response:
making the threat automated and not dependent on the behaviour of player, automatically occurs if a condition is met etc. Makes the threat more credible. Opp knows itll happen.
-Delegating the deciison: If a player believes the other wont carry out the threat, by delegating the decision to another person who the player recieving the threat is certain will carry it out, will make the threat more credible. (delegate the carrying out of threat to anothe person)
-Establish a reputation: with repeated games your opponent might know and understand if you have preiviously carried out threats and promises in previous roudns, establishing a reputation by previously carrying out threats, maybe smaller threats to build reputation may make the threats more credible in the future.
-Appearing irrational. By appearing irrational the threat looks more credible to the other player, a threat in which a rational player woulny of carried out. Eg) the robber acting crazy in the mugger game
-Writing a contract- Make a promise credible by making a contractual agreement. Legal binding contract to prevent deviation and encourage the promise is carried out.
-3rd party fine if dont carry a threat out, damage social reputation make a socail claim thay will carry out etc.
Define salami tactics, how its a method to avoid threat and how to prevent opponent doing when making threats
Salami tactics” refer to a strategy of achieving a goal gradually and stealthily by dividing and conquering opposition, similar to slicing off thin pieces of salami to avoid triggering resistance or detection.
-Allows a threat/carrying out moves to be avoided by making small steps/moves, with each small step not justifiable for a response from the opp to respond.
-To prevent opponent using salami tactics, set multiple threats rather than one large one with relating to smaller consequences. And carry out if opponent crosses the small line, cuts off a salami slice.
check game is zero sum
To check if a game is zero-sum, add up the payoffs of all players for each outcome, and if the sum is always zero, the game is zero-sum.
3 player game table, collumn page and row + finding nash
-create separate tables (pages) for each strategy of the third player, while the rows and columns represent the strategies of the first two players, with each cell containing the payoff triplet corresponding to all three players’ strategies
eg) two strats for eacg player help or not help, two tables one for when third player helps and another for when not help.
-NE found by going through the payoffs of each outcome (eg) H,H, NH) and determine if any player has an incentice to switch. even page player
formula for number of strategies game in a simultenous game
TotalStrategies
product of all number of strats players have, eg) 4If there are 2 players:
Player 1 has 3 strategies.
Player 2 has 2 strategies.
The total number of strategy combinations would be:
3
×
2
=
6
TotalStrategies=3×2=6
method of finding nas hequiblrium with joint profits
-firms maximise joint profits by setting optimal prices, to find these prices maximise total profit function in respect to each quanity or price etc.
