The Chain Store's Twenty Markets

A chain store has a branch in each of 20 towns. In turn, in towns 1, 2, ..., 20, a different potential competitor decides whether to enter. Each entrant observes everything that happened in earlier towns. In one town the payoffs (entrant, chain store) are: the entrant stays out: (1, 5); the entrant enters and the chain store accommodates: (2, 2); the entrant enters and the chain store fights: (0, 0). Each town's game is played once, the chain store maximises the sum of its payoffs over all 20 towns, and every entrant maximises his own payoff. Everyone is rational and the game tree is common knowledge. What total payoff does the chain store earn in the subgame-perfect equilibrium?

• graph theory
• information
• nash equilibrium

Source: Selten's chain-store paradox (1978), in a simplified numerical form. Statement written for AxiomIQ.