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2015•RePEc: Research Papers in EconomicsRequires access

On dynamic games with randomly arriving players

Pierre Bernhard, Marc Deschamps

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Abstract

We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the gamerandomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number ofplayers present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. As illustrations, we discuss some examples relating to oligopoly theory (Cournot, Stackelberg, cartel).

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What this paper is about

We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the gamerandomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number ofplayers present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. As illustrations, we discuss some examples relating to oligopoly theory (Cournot, Stackelberg, cartel).

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Available abstract

We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the gamerandomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number ofplayers present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. As illustrations, we discuss some examples relating to oligopoly theory (Cournot, Stackelberg, cartel).

Key concepts: Mathematical economics, Cournot competition, Sequential game, Stochastic game, Stackelberg competition, Repeated game, Cartel, Oligopoly

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