@Article{banerjee07a,
  author =	 {Dipyaman Banerjee and Sandip Sen},
  title =	 {Reaching pareto-optimality in prisoner's dilemma using conditional joint action learning},
  journal =	 {Autonomous Agents and Multi-Agent Systems},
  volume =	 15,
  number =	 1,
  year =	 2007,
  issn =	 {1387-2532},
  pages =	 {91--108},
  doi =		 {10.1007/s10458-007-0020-8},
  publisher =	 {Kluwer Academic Publishers},
  address =	 {Hingham, MA, USA},
  abstract =	 {We consider the learning problem faced by two
                  self-interested agents repeatedly playing a
                  general-sum stage game. We assume that the players
                  can observe each other's actions but not the payoffs
                  received by the other player. The concept of Nash
                  Equilibrium in repeated games provides an
                  individually rational solution for playing such
                  games and can be achieved by playing the Nash
                  Equilibrium strategy for the single-shot game in
                  every iteration. Such a strategy, however can
                  sometimes lead to a Pareto-Dominated outcome for
                  games like Prisoner's Dilemma. So we prefer learning
                  strategies that converge to a Pareto-Optimal outcome
                  that also produces a Nash Equilibrium payoff for
                  repeated two-player, n-action general-sum games. The
                  Folk Theorem enable us to identify such outcomes. In
                  this paper, we introduce the Conditional Joint
                  Action Learner (CJAL) which learns the conditional
                  probability of an action taken by the opponent given
                  its own actions and uses it to decide its next
                  course of action. We empirically show that under
                  self-play and if the payoff structure of the
                  Prisoner's Dilemma game satisfies certain
                  conditions, a CJAL learner, using a random
                  exploration strategy followed by a completely greedy
                  exploitation technique, will learn to converge to a
                  Pareto-Optimal solution. We also show that such
                  learning will generate Pareto-Optimal payoffs in a
                  large majority of other two-player general sum
                  games. We compare the performance of CJAL with that
                  of existing algorithms such as WOLF-PHC and JAL on
                  all structurally distinct two-player conflict games
                  with ordinal payoffs.},
  url = 	 {http://jmvidal.cse.sc.edu/library/banerjee07a.pdf},
  keywords = 	 {multiagent learning}
}