Browsing by Subject "Repeated games"

Now showing 1 - 3 of 3

Open Access
Order of limits in reputations
(Springer, 2016) Dalkıran, N. A.
The fact that small departures from complete information might have large effects on the set of equilibrium payoffs draws interest in the adverse selection approach to study reputations in repeated games. It is well known that these large effects on the set of equilibrium payoffs rely on long-run players being arbitrarily patient. We study reputation games where a long-run player plays a fixed stage-game against an infinite sequence of short-run players under imperfect public monitoring. We show that in such games, introducing arbitrarily small incomplete information does not open the possibility of new equilibrium payoffs far from the complete information equilibrium payoff set. This holds true no matter how patient the long-run player is, as long as her discount factor is fixed. This result highlights the fact that the aforementioned large effects arise due to an order of limits argument, as anticipated. Â© 2016, Springer Science+Business Media New York.
Open Access
Social norms and choice: a weak folk theorem for repeated matching games
(Springer, 2007) Hasker, K.
A folk theorem which holds for all repeated matching games is established. The folk theorem holds any time the stage game payoffs of any two players are not affinely equivalent. The result is independent of population size and matching rule-including rules that depend on players choices or the history of play. © 2007 Springer Verlag.
Open Access
Stochastic control approach to reputation games
(IEEE, 2020) Nuh Aygün, Dalkıran; Yüksel, S.
Through a stochastic-control-theoretic approach, we analyze reputation games, where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the information of the short-lived players is nested in that of the long-lived player. This nested information structure is obtained through an appropriate monitoring structure. Under this monitoring structure, we show that, given mild assumptions, the set of perfect Bayesian equilibrium payoffs coincides with Markov perfect equilibrium payoffs, and hence, a dynamic programming formulation can be obtained for the computation of equilibrium strategies of the strategic long-lived player in the discounted setup. We also consider the undiscounted average-payoff setup, where we obtain an optimal equilibrium strategy of the strategic long-lived player under further technical conditions. We then use this optimal strategy in the undiscounted setup as a tool to obtain a tight upper payoff bound for the arbitrarily patient long-lived player in the discounted setup. Finally, by using measure concentration techniques, we obtain a refined lower payoff bound on the value of reputation in the discounted setup. We also study the continuity of equilibrium payoffs in the prior beliefs.