We offer a new formal criterion for agent-centric learning in multi-agent systems, that is, learning that maximizes one's rewards in the presence of other agents who might also be learning (using the same or other learning algorithms). This new criterion takes in as a parameter the class of opponents. We then provide a modular approach for achieving effective agent-centric learning; the approach consists of a number of basic algorithmic building blocks, which can be instantiated and composed differently depending on the environment setting (for example, 2-versus n-player games) as well as the target class of opponents. We then provide several specific instances of the approach: an algorithm for stationary opponents, and two algorithms for adaptive opponents with bounded memory, one algorithm for the nplayer case and another optimized for the 2-player case. We prove our algorithms correct with respect to the formal criterion, and furthermore show the algorithms to be experimentally effective via comprehensive computer testing.
We address the problem of learning in repeated n-player (as opposed to 2-player) general-sum games, paying particular attention to the rarely addressed situation in which there are a mixture of agents of different types. We propose new criteria requiring that the agents employing a particular learning algorithm work together to achieve a joint best-response against a target class of opponents, while guaranteeing they each achieve at least their individual security-level payoff against any possible set of opponents. We then provide algorithms that provably meet these criteria for two target classes: stationary strategies and adaptive strategies with a bounded memory. We also demonstrate that the algorithm for stationary strategies outperforms existing algorithms in tests spanning a wide variety of repeated games with more than two players.
We investigated the existence of fair seeding in knockout tournaments. We define two fairness criteria, both adapted from the literature: envy-freeness and order preservation. We show how to achieve the first criterion in tournaments whose structure is unconstrained, and prove an impossibility result for balanced tournaments. For the second criterion we have a similar result for unconstrained tournaments, but not for the balanced case. We provide instead a heuristic algorithm which we show through experiments to be efficient and effective. This suggests that the criterion is achievable also in balanced tournaments. However, we prove that it again becomes impossible to achieve when we add a weak condition guarding against the phenomenon of tournament dropout.
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