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3

The following proposition is well known: If a stage game $G$ has a unique Nash equilibrium, then for any finite $T$, the repeated game $G(T)$ has a unique subgame perfect equilibrium outcome in which the Nash equilibrium of $G$ is played in every stage. Since your stage game has a unique NE of $(T,R)$, this must be the outcome of the SPE of any finitely ...

3

I don't think behavioral game theory is inspired much by biology. Rather it's motivated by the discrepancies between theoretical predictions and the choices observed in lab experiments. It seeks to improve the predictive accuracy of game theoretic models by introducing behavioral assumptions that allow players to behave in ways different from the traditional ...

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It is a convoluted definition because condition 3: "At all $h$, if there exists a previously unclinchable payoff x that becomes impossible for agent $i_h$ at $h$, then $C_i^\subset (h) \subseteq C_i^h (h)$." means that at every history if there is a payoff that player $i_h$ could not have secured (or clinched), but was feasible at every previous history ...

2

Mixed strategy Nash equilibrium cannot involve strictly dominated strategies. In particular, Cooperate is strictly dominated for player 1 ($6<8$ and $3<4$). Therefore, no $b\in[0,1]$ can make player 1 indifferent between Cooperate and Non-cooperate. You made a mistake by trying to solve for $b$ by equating player 1's expected payoffs from his two pure ...

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