Summary: Suppose two agents play a game, each using a computable algorithm to decide what to do, these algorithms being common knowledge. We show that it is possible to act rationally provided we limit our attention to a natural subset of solvable games and to opponents who use rational algorithms; the outcome is a Nash equilibrium. Going further we show that rationality is possible on many domains of games and opposing algorithms but each domain requires a particular solution algorithm; no one algorithm is rational on all possible domains.