Production Games One of the most famous games is the prisoners'dilemma. This has two players with two strategies each and four associated payoffs for each player. It can be represented by the two-by-two matrix below. 5 0 This is called the normal form or strategic form of the game. All discrete action space games can be represented in such matrices. Action spaces need not be discrete-for cample, firms set quanti d consumers choose bundles of goods ed will be simultaneous moue games. All players make their decision without observing the strategies played by other agents. In many interesting games players do observe some of the actions of others. Firms may make decisions sequentially. Such dynamic games will be considered very briefly Best Responses Suppose a player's opponent in a game plays a particular strategy. What would the player do? The strategy that ises the player's payoff given their opponent's play is a best respon The collection of best responses for each possible action of their opponent is called a best response function-or a reaction function(or even a best reply function). Plotting this gives the reaction What are the best responses in the prisoners'dilemma Common practice is to underline the payoffs corresponding to best responses in such a normal form gameProduction — Games 5 Some Examples • One of the most famous games is the prisoners’ dilemma. This has two players with two strategies each and four associated payoffs for each player. It can be represented by the two-by-two matrix below. C D C 3 3 5 0 D 0 5 1 1 • This is called the normal form or strategic form of the game. • All discrete action space games can be represented in such matrices. Action spaces need not be discrete — for example, firms set quantities and consumers choose bundles of goods. • Most of the games presented will be simultaneous move games. All players make their decision without observing the strategies played by other agents. • In many interesting games players do observe some of the actions of others. Firms may make decisions sequentially. Such dynamic games will be considered very briefly. Production — Games 6 Best Responses • Suppose a player’s opponent in a game plays a particular strategy. What would the player do? The strategy that maximises the player’s payoff given their opponent’s play is a best response. • The collection of best responses for each possible action of their opponent is called a best response function — or a reaction function (or even a best reply function). Plotting this gives the reaction curve. • What are the best responses in the prisoners’ dilemma? C D C 3 3 5 0 D 0 5 1 1 • Common practice is to underline the payoffs corresponding to best responses in such a normal form game