Kevin F. McCardle

The Competitive Newsboy

We consider a competitive version of the classical newsboy problem-in which a firm must choose an inventory or production level for a perishable good with random demand, and the optimal solution is a fractile of the demand distribution-and investigate the impact of competition upon industry inventory. A splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory. We examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium. Our most general result is that if all excess demand is reallocated, i.e., there is perfect substitutability, then competition never leads to a decrease in industry inventory.

Coherent behavior in noncooperative games

Abstract A new concept of mutually expected rationality in noncooperative games is proposed: joint coherence. This is an extension of the “no arbitrage opportunities” axiom that underlies subjective probability theory and a variety of economic models. It sheds light on the controversy over the strategies that can reasonably be recommended to or expected to arise among Bayesian rational players. Joint coherence is shown to support Aumanns position in favor of objective correlated equilibrium, although the common prior assumption is weakened and viewed as a theorem rather than an axiom. An elementary proof of the existence of correlated equilibria is given, and relationships with other solution concepts (Nash equilibrium, independent and correlated rationalizability) are also discussed.

Arbitrage, rationality, and equilibrium

No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.

Comparative statics in non-cooperative games via transfinitely iterated play

Abstract Tarskis fixed point theorem establishes the existence of a Nash equilibrium when (a) each players lattice of strategies is complete and (b) the composite best response function is isotone. Suppose the composite best response function is also isotone in one of the underlying parameters. Then our transfinite variant of iterated best response play is shown to “converge” and to produce an unambiguous comparative statics analysis. The efficacy of this approach is demonstrated with three examples.

Preemption in R&D races

Abstract Fudenberg, Gilbert, Stiglitz and Tirole (1983) consider a patent race in which each firms instantaneous probability of discovering a patentable invention is an increasing function of its cumulative expenditure on RD in particular, we show that for intermediate values of τ it is possible for the follower to ‘spoil’ the race by forcing the leader to drop out.

Strategic uncertain search

Abstract We prove the existence of pure strategy Nash equilibria in a duopoly model of search when the value of an item is revealed only through the costly acquisition of information.