6

A couple hints. Regarding the lower bound on $\epsilon$: What happens if deviation occurs at stage $T$? In other words, there is no opportunity for your so-called "punishment stages". Regarding the upper bound on $\epsilon$: Suppose player 2 deviates at stage $T-1$ but player 1 does not. What must be true about $\epsilon$ in order for player 1 to ...


5

There is also no NE which sustains coopration for more or less the same reason as in the SPNE case. Consider, a PD played twice. A strategy contains five actions, one for each decision node: one in the beginning (empty history) and one for each of the four period-2 histories (CC,CD,DC,DD). I claim that any strategy other than (D;D;D;D;D) is dominated. ...


3

Why don't you attack the problem straighrforwardly and investigate the profitability of a deviation? Suppose there was a Nash equilibrium in which both players decide to stay forever. Both players obtain payoff $\frac{1}{1-d}$ on path. This really is a Nash equilibrium if anf only if there is no profitable deviation. Consider the deviation to quit in the ...


2

In the standard theory of games, simultaneous and sequential games are distinguished by the means of something called "Information Sets". Alluding to the origins of Game Theory (von Neumann and Morgenstern 1944), simultaneous move games can be thought of as special cases of sequential move games. In their landmark work, vN-M give an explicit method ...


Only top voted, non community-wiki answers of a minimum length are eligible