Markov Equilibria in Dynamic Matching and Bargaining Games

Rubinstein and Wolinsky (1990) show that a simple homogeneous market with exogenous matching has continuum of (non-competitive) perfect equilibria, but the unique Markov perfect equilibrium is competitive. By contrast, in the more general case of heterogeneous markets, we show there exists a continuum of (non-competitive) Markov perfect equilibria. However, a refinement of the Markov property, which we call monotonicity, does suffice to guarantee perfectly competitive equilibria, if, and only if, it is monotonic. The monotonicity property is closely related to the concept of Nash equilibrium with complexity costs

Complexity and Efficiency in Repeated Games with Negotiation

This paper considers the "negotiation game" (Busch and Wen, 1995) which combines the features of two-person alternating offers bargaining and repeated games. Despite the forces of bargaining, the negotiation game in general admits a large number of equilibria some of which involve delay in agreement and inefficiency. In order to isolate equilibria in this game, we explicitly consider the complexity of implementing a strategy, introduced in the literature on repeated games played by automata. It turns out that when the players have a preference for less complex strategies (even at the margin) only efficient equilibria survive. Thus, complexity and bargaining in tandem may offer an explanation for co-operation in repeated gamesNegotiation Game, Repeated Game, Bargaining, Complexity, Bounded Rationality, Automaton

Complexity and Efficiency in the Negotiation Game

This paper considers the ``negotiation game'' Busch and Wen (1995)) which combines the features of two-person alternating offers bargaining and repeated games. Despite the forces of bargaining, the negotiation game in general admits a large number of equilibria some of which involve delay and inefficiency. In order to isolate equilibria in this game, we investigate the role of complexity of implementing a strategy, introduced in the literature on repeated games played by automata. It turns out that when the players care for less complex strategies (at the margin) only efficient equilibria survive. Thus, complexity and bargaining in tandem may offer an explanation for co-operation and efficiency in repeated gamesBargaining, Repeated Game, Negotiation Game, Complexity, Automaton

N-Person Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n -person unanimity bargaining game. In particular, the paper provides a justification for stationary equilibrium strategies in the class of games where complexity costs matter. As is well-known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n > 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to strategies that can be implemented by a machine (automaton) and by suitably modifying the definition of complexity for the purpose of analysing a single extensive form, we find that complexity costs do not reduce the range of possible allocations but they do limit the amount of delay that can occur in any agreement. In particular, we show that in any n-player game, for any allocation z; an agreement on z at any period t can be sustained as a Nash equilibrium of the machine game with complexity costs if and only if t · n: We use the limit on delay result to establish that, in equilibrium, the machines implement stationary strategies. Finally, we also show that noisy Nash equilibrium” with complexity costs sustain only the unique stationary subgame perfect equilibrium allocation.

Complexity and Efficiency in Repeated Games with Negotiation

This paper considers the "negotiation game" (Busch and Wen, 1995) which combines the features of two-person alternating offers bargaining and repeated games. Despite the forces of bargaining, the negotiation game in general admits a large number of equilibria some of which involve delay in agreement and inefficiency. In order to isolate equilibria in this game, we explicitly consider the complexity of implementing a strategy, introduced in the literature on repeated games played by automata. It turns out that when the players have a preference for less complex strategies (even at the margin) only efficient equilibria survive. Thus, complexity and bargaining in tandem may offer an explanation for co-operation in repeated gamesNegotiation Game, Repeated Game, Bargaining, Complexity, Bounded Rationality, Automaton

Herd Behavior in Efficient Financial Markets

Rational herd behavior and informationally efficient security prices have long been considered to be mutually exclusive but for exceptional cases. In this paper we describe conditions on the underlying information structure that are necessary and sufficient for informational herding. Employing a standard sequential security trading model, we argue that people may be subject to herding if and only if there is sufficient amount of noise and, loosely, their information leads them to believe that extreme outcomes are more likely than moderate ones. We then show that herding has a significant effect on prices: prices can move substantially during herding and they become more volatile than if there were no herding. Furthermore, herding can be persistent and can affect the process of learning. We also characterize conditions for contrarian behavior. Our analysis suggests that herding (and contrarian behavior) may be more pervasive than was originally thought. Hence, the paper provides a new perspective on herding in financial markets with efficient pricesMicrostructure, Sequential Trades, Herding, Monotone Likelihood

Distributing Awards Efficiently: More on King Solomon's Problem

We consider a multi-award generalisation of King Solomon's problem: k identical and indivisible awards should be distributed among agents, k 1) prizes efficiently in sub-game perfect equilibria without any monetary transfers in equilibrium. Finally, in the multi-awards case we relax the complete information assumption and achieve implementation of efficient allocation by iterative elimination of weakly dominated strategies, using generalisation of Olszewski's (2003) mechanism

The bounded memory folk theorem

We show that the Folk Theorem holds for n-player discounted repeated games with bounded-memory pure strategies. Our result requires each player’s payoff to be strictly above the pure minmax payoff but requires neither time-dependent strategies, nor public randomization, nor communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions

Bargaining and Markets: Complexity and the Walrasian Outcome

Rubinstein and Wolinsky (1990b) consider a simple decentralized market in which agents either meet randomly or choose their partners volunatarily and bargain over the terms on which they are willing to trade. Intuition suggests that if there are no transaction costs, the outcome of this matching and bargaining game should be the unique competitive equilibrium. This does not happen. In fact, Rubinstein and Wolinsky show that any price can be sustained as a sequential equilibrium of this game. In this paper, I consider Rubinstein and Wolinsky's model and show that if the complexity costs of implementing strategies enter players' preferences (lexicographically), together with the standard payoff in the game, then the only equilibrium that survives is the unique competitive outcome. This will be done both for the random matching and for the voluntary matching models. Thus the paper demonstrates that complexity costs might have a role in providing a justification for the competitive outcome.Bargaining, matching, complexity, automata, bounded rationality, competitive outcome, Walrasian equilibrium