Social Learning and the Exploration-Exploitation Tradeoff

Cultures around the world show varying levels of conservatism. While maintaining traditional ideas prevents wrong ones from being embraced, it also slows or prevents adaptation to new times. Without exploration there can be no improvement, but often this effort is wasted as it fails to produce better results, making it better to exploit the best known option. This tension is known as the exploration/exploitation issue, and it occurs at the individual and group levels, whenever decisions are made. As such, it is has been investigated across many disciplines. We extend previous work by approximating a continuum of traits under local exploration, employing the method of adaptive dynamics, and studying multiple fitness functions. In this work, we ask how nature would solve the exploration/exploitation issue, by allowing natural selection to operate on an exploration parameter in a variety of contexts, thinking of exploration as mutation in a trait space with a varying fitness function. Specifically, we study how exploration rates evolve by applying adaptive dynamics to the replicator-mutator equation, under two types of fitness functions. For the first, payoffs are accrued from playing a two-player, two-action symmetric game, we consider representatives of all games in this class, including the Prisoner’s Dilemma, Hawk-Dove, and Stag Hunt games, finding exploration rates often evolve downwards, but can also undergo neutral selection as well depending on the games parameters or initial conditions. Second, we study time dependent fitness with a function having a single oscillating peak. By increasing the period, we see a jump in the optimal exploration rate, which then decreases towards zero as the frequency of environmental change increases. These results establish several possible evolutionary scenarios for exploration rates, providing insight into many applications, including why we can see such diversity in rates of cultural change.