Game Theory Flashcards
What is the purpose of studying game theory/strategic interaction?
So far, our analysis has been about independent decision making
It doesn’t consider how our Marginal Benefit/Marginal Cost are impacted by the decisions of others
Now we will examine how we interact with each other and how other’s decisions impact our decisions
The benefits and costs (payoffs) depend on the actions of others
What are the three elements of game theory?
Players
One player is a row player, while another player is a column player
Strategies
These are choices/options that the player has available (Si)
Payoffs
Costs and benefits associated with the strategy
These depend on our own actions, but also on the actions of others
What are simultaneous games and one shot games?
Players make decisions/choose strategies at the same time
Each player has perfect information; they know all the choices their opponent has and the associated payoffs
There are also one-shot games; played only once
What does a payoff matrix look like?
Explore the prisoner’s dilemma, and explain the concept of a dominant strategy
Bonnie and Clyde both have a DOMINANT STRATEGY to confess
A dominant strategy is a situation where the players have no incentive to change their strategy
It is their best response regardless of what the other player chooses
This means that the equilibrium outcome is (confess, confess)
When both players have a dominant strategy, the resulting outcome is a single dominant strategy equilibrium
Explore the ‘Battle of the Sexes’ and explain the concept of a Nash Strategy
The best response given what the other player does
Because no player has a dominant strategy, the result is multiple equilibria (a Nash Equilibrium)
In the above example, the equilibrium is either (Boxing, Boxing) OR (Opera, Opera)
Explore how having a dominant strategy can lead to worse outcomes for both parties (with reference to the tragedy of the commons)
The tragedy of the commons is that the equilibrium that the players end up with is not the best equilibrium for them overall
Explore the concept of zero-sum games
Occurs when the sum of the payoffs comes to zero
These are also known as anti-coordination games
Neither party has a dominant strategy
There is no equilibrium, because no point is where either party is positive/equal
In these cases, the best strategy is to have no strategy (random choice, mixed strategy)
Having a strategy means that your opponent will simply choose the opposite
In repeated games, what are the options for collusion among the players?
1) Tit-For-Tat
1st Time Co-Operate
Every subsequent round do what other player did in previous round
2) Threat Or Punishment
Needs a stable set of players (ideally two)
Significant stake in what happens in the future
What is the impact of a game having an infinite number of rounds?
Each round/time we play leads to developing a reputation
The repetition provides opportunities to collude
Collusion will lead to the parties choosing the best outcome for both players
What is the impact of a game having a finite number of rounds?
Incentive for both players to cheat in final round
If you know that there is no cooperation in the last round, to get higher payoff, you need to cheat in the next-to-last round
This results in the game unravelling
Different outcomes will result from how long people think that the game will go on
What are sequential games, and what impact can they have on outcomes?
Not simultaneous, meaning that an order of play is specified
A sequential game can allow for the parties to find an equilibrium
There can be a first move advantage in a sequential game
A way around this is through a ‘credible threat’ in which the second player attempts to influence the actions of the first player
Another option is a ‘commitment strategy’ changing the incentives to make threats and promises credible – an example of this are tips as a percentage of wages for wait staff
How does the ultimatum game reveal the complexities of game theory?
In the experiment, one player (the proposer) is endowed with a sum of money and asked to split it between themselves and an anonymous player (the responder)
The responder may either accept the allocator’s proposal or reject it, in which case neither of the players will receive anything
Common sense says that the responder should accept any amount, meaning that the proposer should give them the minimum amount
What does happen is that the proposer offers more than a ‘token’ amount
One reason for this is that they believe that such a person will reject it (knowing that the responder may not be rational
Another explanation is that the simply am/want to be perceived as nice
There is the potential of a social preference for equity
What is ‘Level-K’ thinking?
We process a lot of information when making decisions and reason complexly – not just at a single ‘level’
K-O = not really thinking (random choices)
K-1 = I think others are level 0, so based on their random choice, I’ll choose…
K-2 = I think others are level 1 – they think everyone is random so they’kk choose based on that, so I choose…
So on for each level, you assume others are a level less and choose your best response based on that
