Today’s Nobel and the Future of Settlement Bargaining
This year’s Nobel Memorial Prize in Economic Sciences was awarded today to Paul Milgrom and Robert Wilson for their work on auction theory and improvement of auction designs. (See Marginal Revolution’s excellent coverage here, here, and here.) Milgrom and Wilson not only made major contributions to auction theory, but also designed auctions that the Federal Communications Commission used to distribute spectrum. The study of auctions today is advanced by a marriage of economics and computer science known as algorithmic game theory. (See here for a book-length introduction.)
Another strand of algorithmic game theory involves identification of equilibria in games, including imperfect information games. Players’ strategies in a game form a Nash equilibrium if each player, knowing the strategy of the other, will retain her strategy rather than switch to some other strategy. A strategy is a function that maps every potential game situation into a probability distribution of actions to take in that situation. Much of the progress in algorithmic game theory in recent years has used the game poker as a test bed. Poker is a game of asymmetric information. One cannot simply reason from the current state of the game to the end of the game, as in chess. Rather, a poker player must assess the different possible current states of the game, an assessment that depends on analysis of an opposing player’s moves. Because those moves were made also thinking both retrospectively and prospectively, players’ strategies in any game state potentially influence the optimal strategy even at entirely different game states.
An important paper, published in 2007 by Martin Zinkevich et al., introduces an algorithm known as counterfactual regret minimization to address this challenge. The literature has offered many variations on and improvements to this algorithm. Marc Lanctot’s dissertation is an excellent introduction to counterfactual regret minimization. Recent advances have involved incorporation of deep neural network learning (see Noam Brown et al.’s contribution here and Eric Steinberger’s here), which allows for machine learning of strategies in games where there are too many ways the game can unfold for a computer to traverse efficiently every possible permutation of moves in the game tree.
Like poker, litigation is a game of asymmetric information. In a simple lawsuit between the plaintiff and the defendant, each side knows what it thinks about how strong the case is, but it doesn’t know what the other party thinks. Differences in evaluation may result from differen
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