Learning in a Black Box

Many interactive environments can be represented as games, but they are so large and complex that individual players are in the dark about what others are doing and how their own payo s are a ected. This paper analyzes learning behavior in such 'black box' environments, where players' only source of information is their own history of actions taken and payoff s received. Speci fically we study repeated public goods games, where players must decide how much to contribute at each stage, but they do not know how much others have contributed or how others' contributions a effect their own payoff s. We identify two key features of the players' learning dynamics. First, if a player's realized payoff increases he is less inclined to change his strategy, whereas if his realized payo ff decreases he is more inclined to change his strategy. Second, if increasing his own contribution results in higher payoff s he will tend to increase his contribution still further, whereas the reverse holds if an increase in contribution leads to lower payo ffs. These two e ffects are clearly present when players have no information about the game; moreover they are still present even when players have full information. Convergence to Nash equilibrium occurs at about the same rate in both situations.