Discussion and interpretation of Nash equilibria (2) Pareto-optimal Nash equilibria are likely focal. Thomas Schelling(1960 )suggested that in the case of multiple equilibria, expectations may be coordinated by focal points. Focal points are attributes of the le strategies or payoffs that are conspicuous or prominent and therefore coordinate expectations and choices of players when cultural and historical norms determine what is focalar there are multiple Nash equilibria. Schelling argued tha Matching pennies is an example of a zero sum,or strictly-competitive, game. This means that for any outcome. th he gain to one player exactly equals the loss of the other player. Unlike the prisoners dilemma or the battle of the sexes, there is no common interest, just rivate interest
Discussion and interpretation of Nash equilibria (2) • Pareto-optimal Nash equilibria are likely focal. Thomas Schelling (1960) suggested that in the case of multiple equilibria, expectations may be coordinated by focal points. Focal points are attributes of the strategies or payoffs that are conspicuous or prominent and therefore coordinate expectations and choices of players when there are multiple Nash equilibria. Schelling argued that cultural and historical norms determine what is focal. • Matching pennies is an example of a zero sum, or strictly-competitive, game. This means that for any outcome, the gain to one player exactly equals the loss of the other player. Unlike the prisoners’ dilemma or the battle of the sexes, there is no common interest, just private interest
Hockey Ballet Hockey 2.2 0.0 Ballet 0, 0 3.3 Pareto-dominant focal point Heads Tails Heads Tails Matching pennies
2,2 0,0 0,0 3,3 1,-1 -1,1 -1,1 1,-1 Hockey Ballet Hockey Ballet Pareto-dominant focal point Heads Tails Heads Tails Matching pennies
Discussion and interpretation of Nash equilibria 3) Interpretation and justification of Nash equilibrium The set of rationalizable strategies are those that survive iterative elimination of never-best responses a rationalizable strategy can be justified on the basis of conjectures or expectations about opponents that do not involve the rival playing a never-best response
Discussion and interpretation of Nash equilibria (3) • Interpretation and justification of Nash equilibrium • The set of rationalizable strategies are those that survive iterative elimination of never-best responses. A rationalizable strategy can be justified on the basis of conjectures or expectations about opponents that do not involve the rival playing a never-best response
Discussion and interpretation of Nash equilibria (4) The difference between the Nash equilibrium strategies and the set of rationalizable strategies is that the strategies that constitute a Nash equilibrium require that the expectations not only be reasonable, but correct In a Nash equilibrium, it is optimal for all players to play as predicted and expectations are correct The assumptions that players are rational and have common knowledge is not enough to justify using Nash equilibrium to make predictions regarding play of a game One approach is to work backwards and argue that if there is an obvious way to play a game, it must be a Nash equilibrium
Discussion and interpretation of Nash equilibria (4) • The difference between the Nash equilibrium strategies and the set of rationalizable strategies is that the strategies that constitute a Nash equilibrium require that the expectations not only be reasonable, but correct. • In a Nash equilibrium, it is optimal for all players to play as predicted and expectations are correct. • The assumptions that players are rational and have common knowledge is not enough to justify using Nash equilibrium to make predictions regarding play of a game. • One approach is to work backwards and argue that if there is an obvious way to play a game, it must be a Nash equilibrium
Discussion and interpretation of nash equilibria(5) 4 reasons why there might be an obvious way to play the game 1 focal points Cultural and historical factors can not only coordinate expectations between multiple Nash equilibria, but they might also coordinate expectations on the Nash equilibrium strategies 2 self-enforcing agreements The only agreements that will survive the playing of the game are agreements to play Nash equilibrium strategies. Only at Nash equlibria wil no player have an incentive to deviate and break the agreement
Discussion and interpretation of Nash equilibria (5) • 4 reasons why there might be an obvious way to play the game: • 1 focal points • Cultural and historical factors can not only coordinate expectations between multiple Nash equilibria, but they might also coordinate expectations on the Nash equilibrium strategies. • 2 self-enforcing agreements • The only agreements that will survive the playing of the game are agreements to play Nash equilibrium strategies. Only at Nash equilibria will no player have an incentive to deviate and break the agreement