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Subgame Perfect Equilibria in Discounted Stochastic Games
Tekijät: Mitri Kitti
Kustantaja: Aboa Center of Economics
Kustannuspaikka: Aboa Centre for Economics, Discussion paper No. 87
Julkaisuvuosi: 2013
Artikkelin numero: No 87
eISSN: 1796-3133
Verkko-osoite: http://www.ace-economics.fi/kuvat/dp87.pdf
Tiivistelmä
This paper considers policies and payoffs corresponding to subgame
perfect equilibrium strategies in discounted stochastic games with finitely
many states. It is shown that a policy is induced by an equilibrium
strategy if and only if it can be supported with the threat of reverting to
the induced policy that gives the least equilibrium payoff for the deviator.
It follows that the correspondence of subgame perfect equilibrium
payoffs is the largest fixed-point of a correspondence-valued operator
defined by the players’ incentive compatibility conditions. Moreover,
the fixed-point iteration converges to the equilibrium payoff correspondence.
This paper considers policies and payoffs corresponding to subgame perfect equilibrium strategies in discounted stochastic games with finitely many states. It is shown that a policy is induced by an equilibrium strategy if and only if it can be supported with the threat of reverting to the induced policy that gives the least equilibrium payoff for the deviator. It follows that the correspondence of subgame perfect equilibrium payoffs is the largest fixed-point of a correspondence-valued operator defined by the players’ incentive compatibility conditions. Moreover, the fixed-point iteration converges to the equilibrium payoff correspondence.
This paper considers policies and payoffs corresponding to subgame
perfect equilibrium strategies in discounted stochastic games with finitely
many states. It is shown that a policy is induced by an equilibrium
strategy if and only if it can be supported with the threat of reverting to
the induced policy that gives the least equilibrium payoff for the deviator.
It follows that the correspondence of subgame perfect equilibrium
payoffs is the largest fixed-point of a correspondence-valued operator
defined by the players’ incentive compatibility conditions. Moreover,
the fixed-point iteration converges to the equilibrium payoff correspondence.
This paper considers policies and payoffs corresponding to subgame perfect equilibrium strategies in discounted stochastic games with finitely many states. It is shown that a policy is induced by an equilibrium strategy if and only if it can be supported with the threat of reverting to the induced policy that gives the least equilibrium payoff for the deviator. It follows that the correspondence of subgame perfect equilibrium payoffs is the largest fixed-point of a correspondence-valued operator defined by the players’ incentive compatibility conditions. Moreover, the fixed-point iteration converges to the equilibrium payoff correspondence.
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