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Example 1: Two-Stage Repeated Game with Multiple Nash Equilibria Example 1 shows a two-stage repeated game with multiple pure strategy Nash equilibria. Because these equilibria differ markedly in terms of payoffs for Player 2, Player 1 can propose a strategy over multiple stages of the game that incorporates the possibility for punishment or ...
For instance if a player prefers "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the strategy profile is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to the other players' strategies in that equilibrium ...
This equilibrium can be found by iterated elimination of weakly dominated strategies. [4] Intuitively, guessing any number higher than 2 / 3 of what you expect others to guess on average cannot be part of a Nash equilibrium. The highest possible average that would occur if everyone guessed 100 is 66 + 2 / 3 .
Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same for all players, it is listed here. Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every ...
The pure Nash equilibria are the points in the bottom left and top right corners of the strategy space, while the mixed Nash equilibrium lies in the middle, at the intersection of the dashed lines. Unlike the pure Nash equilibria, the mixed equilibrium is not an evolutionarily stable strategy (ESS).
Anshelevich et al. studied network design games and showed that a pure strategy Nash equilibrium always exists and the price of stability of this game is at most the nth harmonic number in directed graphs. For undirected graphs Anshelevich and others presented a tight bound on the price of stability of 4/3 for a single source and two players case.
If δ is close to 1, this outweighs any finite one-stage gain, making the strategy a Nash equilibrium. An alternative statement of this folk theorem [ 4 ] allows the equilibrium payoff profile u to be any individually rational feasible payoff profile; it only requires there exist an individually rational feasible payoff profile that strictly ...
The solution for player 2 is equivalent. Using numerical values b 1 = 2, b 2 = −1, w = 3, this example transforms into a simple battle of the sexes, as shown in Figure 2. The game has two pure Nash equilibria, (+1, +1) and (−1, −1). These are also the local maxima of the potential function (Figure 3).