Escalating games: how intermediate levels of conflict affect stability of cooperation

We argue that cooperation can become more fragile if (i) there are sufficiently many intermediate levels of cooperation and (ii) players cannot respond with large punishments to small deviations. Such disproportional punishments can be perceived as unreasonable or players can face external constraints---political checks, negative publicity, etc. Specifically, we show that regardless of how patient the players are, any prisoner's dilemma game can be extended with intermediate levels of cooperation in such a way that full conflict is the only equilibrium outcome of the extended game.