Infinite sequential games with real-valued payoffs

We investigate the existence of certain types of equilibria (Nash, ε-Nash, subgame perfect, ε-subgame perfect) in infinite sequential games with real-valued payoff functions depending on the class of payoff functions (continuous, upper semi-continuous, Borel) and whether the game is zero-sum. Our results hold for games with two or up to countably many players. Several of these results are corollaries of stronger results that we establish about equilibria in infinite sequential games with some weak conditions on the occurring preference relations. We also formulate an abstract equilibrium transfer result about games with compact strategy spaces and open preferences. Finally, we consider a dynamical improvement rule for infinite sequential games with continuous payoff functions.