Game Theory Flashcards
Game theory
- A science of strategic decision making
- Determines mathematically and logically the actions that ‘players’ should take to secure the best outcome for themselves
- All games share the common feature of interdependence (The outcome for each participant depends upon the choices (strategies) of all )
5 elements of the game
1, The players
2, A complete description of what the players can do – the set of all possible actions
3, The information that players have available when choosing their actions
4, A description of the payoff consequences for each player for every possible combination of actions chosen by all players playing the game
5, A description of all players’ preferences over payoffs
Sequential games
the players move in sequence, each aware of the others’ previous actions.
We determine each player’s best strategy by looking ahead to every possible outcome
Ex: Chess
Simultaneous game
The players act at the same time, each ignorant of the others’ actions, each is aware that there are other players who, in turn, are similarly aware, and so on.
The game is ‘solved’ when it reaches a Nash equilibrium
Types of Outcome
- Non zero sum games
- Zero sum games
Non zero sum games
Correlated outcomes
- Mutual gain (Positive sum games)
- Mutual harm (Negative sum games)
A game is non-zero-sum, if players interests are not always in direct conflict, so that there are opportunities for both to gain
Zero sum games
The interests of the players conflict totally. One persons gain is always another persons loss
A zero-sum game is one in which the players’ interests are in direct conflict, e.g. in football, one team wins and the other loses; payoffs sum to zero
“Rock, Scissors, Paper”
- If players adopt the same strategy, no payments are made
- In other cases, the payoffs indicate payment from the loser to winner under the usual hierarchy
In this game there are no Nash Equilibria
The Prisoners’ Dilemma Game
- Example of Non-Zero Sum Game
- Players choose actions simultaneously without knowing the action chosen by the other
- A game is non-zero-sum, if players interests are not always in direct conflict, so that there are opportunities for both to gain
Battle of the Sexes
Each Nash Equilibrium is equally satisfying
- Reconciling interests?
- Who decides?
Ice Cream Seller
http://www.youtube.com/watch?v=jILgxeNBK_8
This explains the counter intuitive clustering of ice cream sellers close to one another, rather than being spread out across the beach
Chicken
The principle of the game is that while each player prefers not to yield to the other, the worst possible outcome occurs when both players do not yield.
Strategies
- Strategies will depend on whether the game is one-shot or repeated
- How do strategies change when the game is repeated?
Repeated Game Strategies
- The sequential nature of the relationship allows for the adoption of strategies that are contingent on the actions chosen in previous plays of the game
- When players interact by playing a similar stage game (such as the prisoner’s dilemma) numerous times, the game is called a repeated game
- Repeated games encourage cooperation and/or avoidance
- A repeated game allows for a strategy to be contingent on past moves, thus allowing for reputation effects and retribution
- In infinitely repeated games there are trigger strategies such as equivalent retaliation
Assumptions
- Players have perfect information if they know exactly what has happened every time a decision needs to be made, e.g. in Chess
- Otherwise, the game is one of imperfect information
- Payoffs are known and fixed
- People treat expected payoffs the same as certain payoffs (they are risk neutral)
- All players behave rationally (seek to maximize payoff)
- The rules of the game are common knowledge
+ Each player knows the set of players, strategies and payoffs from all possible combinations of strategies: call this information “X”
+ Each player knows that all players know X, that all players know that all players know X, that all players know.., ad infinitum
