By Lucrecia Crider
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Extra resources for Introducing game theory and its applications
However, if there are infinitely many Woodin cardinals with a measurable above them all, then L(R) is a model of ZF that satisfies AD. Consequences of determinacy Regularity properties for sets of reals If A is a subset of Baire space such that the Banach-Mazur game for A is determined, then either II has a winning strategy, in which case A is meager, or I has a winning strategy, in which case A is comeager on some open neighborhood . This does not quite imply that A has the property of Baire, but it comes close: A simple modification of the argument shows that if Γ is an adequate pointclass such that every game in Γ is determined, then every set of reals in Γ has the property of Baire.
Then, the choices are revealed and each player's points total is affected according to the payoff for those choices. Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points. Now, in this example game both players know the payoff matrix and attempt to maximize the number of their points. What should they do? " With similar reasoning, Blue would choose action C. If both players take these actions, Red will win 20 points. But what happens if Blue anticipates Red's reasoning and choice of action 1, and goes for action B, so as to win 10 points?
6 - Reaction correspondence for 2x2 coordination games. e. cross Coordination and equilibrium selection Games like the driving example above have illustrated the need for solution to coordination problems. Often we are confronted with circumstances where we must solve coordination problems without the ability to communicate with our partner. Many authors have suggested that particular equilibria are focal for one reason or another. For instance, some equilibria may give higher payoffs, be naturally more salient, may be more fair, or may be safer.