We Can't Argue Forever

We analyze time-costly decision-making in committees by privately informed individuals, such as juries, panels, boards, etc. In the spirit of the Coase Conjecture, we show that the decision is "almost instantaneous" when individuals entertain identical objectives. Delay can only be understood as the outcome of conflicting (biased) objectives.

Subgame Perfect Correlated Equilibria in Repeated Games

Subgame Perfect Correlated Equilibria in Repeated Games by Pavlo Prokopovych and Lones Smith ABSTRACT This paper investigates discounted infinitely repeated games with observable actions extended with an extensive form correlation device. Such games capture situations of repeated interaction of many players who choose their individual actions conditional on both public and private information. At the beginning of each stage, the players observe correlated private messages sent by an extensive form correlation device. To secure a recursive structure, we assume that players condition their play on the prior history of action profiles and the latest private message they have received from the device. Given a public history, the probability distribution on the product of the players' message sets, according to which the device randomly selects private messages to the players, is common knowledge. This leads to the existence of proper subgames and the opportunity to utilize the techniques developed by Abreu, Pearce, Stacchetti (1990) for studying infinitely repeated games with imperfect monitoring. The extensive form correlation devices we consider send players messages confidentially and separately and are not necessarily direct devices. Proposition 1 asserts that, in infinitely repeated games, subgame perfect correlated equilibria have a simple intertemporal structure, where play at each stage constitutes a correlated equilibrium of the corresponding one-shot game. An important corollary is that the revelation principle holds for such games --- any subgame perfect correlated equilibrium payoff can be achieved as a subgame perfect direct correlated equilibrium payoff. We can therefore focus on the recursive structure of infinitely repeated games extended with an extensive form direct correlation device and characterize the set of subgame perfect direct correlated equilibrium payoffs. In the spirit of dynamic programming, we decompose an equilibrium into an admissible pair that consists of a probability distribution on the product of the players' action sets and a continuation value function. This generalization has allowed us to obtain a number of characterizations of the set of subgame perfect equilibrium payoffs. To illustrate a number of important properties of this set, we study two infinitely repeated prisoner's dilemma games. In the first game, the set of subgame perfect correlated equilibrium payoffs strictly includes not only the set of subgame perfect equilibrium payoffs but also the set of subgame perfect public randomization equilibrium payoffs. In the second game, the set of subgame perfect direct correlated equilibrium payoffs is not convex, strictly includes the set of subgame perfect equilibrium payoffs, and is strictly contained in the set of subgame perfect public randomization equilibrium payoffs. The latter is possible since, in the presence of a public randomization device, the history of public messages observed in previous stages is also common knowledge at the beginning of each stage, which is not the case when messages are private.repeated games with observable actions, correlated equilibrium, private information

Assortative Matching and Reputation

Consider Becker's classic 1963 matching model, with unobserved fixed types and stochastic publicly observed output. If types are complementary, then matching is assortative in the known Bayesian posteriors (the 'reputations'). We discover a robust failure of Becker's result in the simplest dynamic two type version of this world. Assortative matching is generally neither efficient nor an equilibrium for high discount factors. In a labor theoretic rationale, we show that assortative matching fails around the highest (lowest) reputation agents for 'low-skill (high-skill) concealing' technologies. We then find that as the number of production outcomes grows, almost all technologies are of either form. Our theory implies the dynamic result that high-skill matches eventually break up. It also reveals that the induced information rents create discontinuities in the wage profile. This in turn produces life-cycle effects: young workers are paid less than their static marginal product, and old workers more.assortative matching, incomplete information, wages, Bayesian posterior, value function

Simultaneous Search

We introduce and solve a new class of "downward-recursive" static portfolio choice problems. An individual simultaneously chooses among ranked stochastic options, and each choice is costly. In the motivational application, just one may be exercised from those that succeed. This often emerges in practice, such as when a student applies to many colleges. We show that a greedy algorithm finds the optimal set. The optimal choices are "less aggressive" than the sequentially optimal ones, but "more aggressive" than the best singletons. The optimal set in general contains gaps. We provide a comparative static on the chosen set.college application, submodular optimization, greedy algorithm, directed search

Regulatory motif discovery using a population clustering evolutionary algorithm

This paper describes a novel evolutionary algorithm for regulatory motif discovery in DNA promoter sequences. The algorithm uses data clustering to logically distribute the evolving population across the search space. Mating then takes place within local regions of the population, promoting overall solution diversity and encouraging discovery of multiple solutions. Experiments using synthetic data sets have demonstrated the algorithm's capacity to find position frequency matrix models of known regulatory motifs in relatively long promoter sequences. These experiments have also shown the algorithm's ability to maintain diversity during search and discover multiple motifs within a single population. The utility of the algorithm for discovering motifs in real biological data is demonstrated by its ability to find meaningful motifs within muscle-specific regulatory sequences

Caller Number Five and related timing games

There are two varieties of timing games in economics: wars of attrition, in which having more predecessors helps, and pre-emption games, in which having more predecessors hurts. This paper introduces and explores a spanning class with rank-order payoffs that subsumes both varieties as special cases. We assume time is continuous, actions are unobserved, and information is complete, and explore how equilibria of the games, in which there is shifting between phases of slow and explosive (positive probability) stopping, capture many economic and social timing phenomena. Inspired by auction theory, we first show how each symmetric Nash equilibrium is equivalent to a different "potential function.'' By using this function, we straightforwardly obtain existence and characterization results. Descartes' Rule of Signs bounds the number of phase transitions. We describe how adjacent timing game phases interact: war of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms. We bound the number of equilibria, and compute the payoff and duration of each equilibrium.Games of timing, war of attrition, preemption game

Aspirational Bargaining

This paper offers a noncooperative behaviourally-founded solution of the complete information bargaining problem where two impatient individuals wish to divide a unit pie. We formulate the game in continuous time, with unrestricted timing and content of offers. Reprising experimental work from 1960, we introduce and explore aspirational equilibrium -- a Markovian refinement of subgame perfection where behaviour is governed by aspiration values (expected payoffs). The analysis is tractable, and generates many intuitive aspects of bargaining absent from the standard temporal monopoly paradigm: wars of attrition explains delay; serious offers are concessions; offers may be turned down, strictly disappointing the proposers, or accepted, strictly helping the proposer. In particular, an endogenous `proposee' advantage arises, as opposed to the hard-wired proposer standard advantage. We find that discounted aspiration values form a martingale, and thereby compute bounds on the expected bargaining duration from observed offers. We also deduce some simple implications about consecutive offers, and relate delay times, offers, and acceptance rates. Finally, we draw into question a traditional comparative static: Ceteris paribus, more impatient players can expect more of the pie.subgame perfect equilibrium, aspiration, extensive form

Assortative Matching, Reputation, and the Beatles Break-Up

Consider Becker's (1973) classic static matching model, with output a stochastic function of unobserved types. Assume symmetric incomplete information about types, and thus commonly observed Bayesian posteriors. Matching is then assortative in these `reputations' if expected output is supermodular in types. We instead consider a standard dynamic version of this world, and discover a robust failure of Becker's global result. We show that as the production outcomes grow, assortative matching is neither efficient nor an equilibrium for high enough discount factors. Specifically, assortative matching fails around the highest reputation agents for `low-skill concealing' technologies. Our theory implies the dynamic result that high-skill matches (like the Beatles) eventually break~up. Our results owe especially to two findings: (a) value convexity due to learning undermines match supermodularity; and (b) for a fixed policy in optimal learning, the second derivative of the value function explodes geometrically at extremes.supermodularity, convexity

Caller Number Five and Related Timing Games

There are two varieties of timing games in economics: Having more predecessors helps in a war of attrition and hurts in a pre-emption game. This paper introduces and explores a spanning class with rank-order payoffs} that subsumes both as special cases. We assume a continuous time setting with unobserved actions and complete information, and explore how equilibria of these games capture many economic and social timing phenomena --- shifting between phases of slow and explosive (positive probability) stopping. Inspired by auction theory, we first show how the symmetric Nash equilibria are each equivalent to a different "potential function". This device straightforwardly yields existence and characterization results. The Descartes Rule of Signs, e.g., bounds the number phase transitions. We describe how adjacent timing game phases interact: War of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms. We bound the number of equilibria, and compute the payoff and duration of each equilibrium.Games of Timing, War of Attrition, Preemption Game.