Appendix C

Game Theory

The figures and text in this appendix are adapted from Murthy and Jack (2014), pp. 80–85, with the permission of Springer.

A game consists of three elements: the players (the decision makers who participate in the game), their strategies (the plans for each player describing what they will do in any situation), and the payoffs they receive for all combinations of strategies.

In any game, an action is the decision that a player makes at a particular point in the game, whereas a strategy specifies what actions the player will take at each point in the game. A solution concept is a technique that is used to predict the outcome (equilibrium) of the game. It identifies the strategies that the players are likely to play in the game.

Game theory problems may be classified in a number of different ways. The timing of actions by the players and also the number of periods during which games are played lead to different solution approaches. In some games, the players may choose their actions simultaneously, so that no player knows exactly what the others have done when they make a decision. Alternatively, in games with sequential timing, the players choose their actions in a predetermined order. These two situations are termed Nash games and Stackelberg games, respectively.

Some games take place during a single time period, whereas others occur over multiple time periods and the actions taken by the players in each period affect the actions and rewards of the players ...

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