For example, in the Prisonerâs Dilemma game, confessing is a Nash equilibrium because it is the best outcome, taking into account the likely actions of others. 24 Game Theory, the Nash Equilibrium, and the Prisonerâs Dilemma Douglas E. Hill 85. The solution to the prisoner's dilemma game is a Nash equilibrium because no player can improve his or her payoff by changing strategy unilaterally. The most famous example of Nash equilibrium is the prisoner's dilemma.In the prisoner's dilemma, two criminals are captured and interrogated separately. To understand the prisonerÊ¼s dilemma is interesting and also problematic, it is useful to introduce the notion of a Nash equilibrium (named after John Nash). Nash Equilibrium for the prisoners dilemma when using mixed strategies. Generally when you learn the prisoner's dilemma it's to demonstrate what a Nash equilibrium actually is - it's entirely possible to set it up so there isn't a Nash equilibrium at all, or indeed so there are 2. Implications Game Theory provides many insights into the behaviour of oligopolists. correct. There are a lot of different ways that humans can interact, so there are a lot of different models. There is no reason that a dominant strategy must exist to have a Nash equilibrium. Repeated Prisonerâs dilemma: In the game known as the Prisonerâs dilemma , the Nash equilibrium is Confess-Confess (defect-defect). Roughly, a Nash equilibrium is a set of strategies for a given task which is such that, given what every other player is doing, no player would be better off by changing his strategy. As weâll see, the Nash equilibrium might not be the best option for the group â or for any individual player. If player A would switch to lie while player B stays with telling the truth player A would get 10 years in prison, so he won't switch. The Nash equilibriumâwhat I call the âstable outcomeââof the prisonerâs dilemma is that both players lose, even though it is entirely possible for them both to win if they had strategically cooperated. If a player does not have a dominant strategy, can the game still have a Nash equilibrium? In any case, no, there isn't always a Nash equilibrium. Game theory models human interactions. Even though each would be â¦ (Econ wonks would say that the outcome isnât Pareto efficient.) Ask Question Asked 7 years, 8 months ago. In the Prisonerâs Dilemma, for example, each prisoner will be better off denying a crime, but both have incentives to confess to it â and together, will double their stays in jail. https://www.khanacademy.org/.../v/prisoners-dilemma-and-nash-equilibrium ... (-1,-6) & (-4, -4) \end{array}  which corresponds to the well-known prisonder's dilemma. Yes. The same holds for player B. The prisoner's dilemma is not a repeated game. 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