Volume 2, Issue 1

We propose an agency model based on competitive markets in order to analyse an economy with several homogeneous principals and heterogeneous agents. We model the principal-agent economy as a two-sided matching game and characterise the set of stable outcomes (equilibria) of this market. In this regard we generalise the assignment game of Shapley and Shubik (1972). Unlike in the standard principal-agent theory, equilibrium payoffs of all the individuals are endogenous, equilibrium contracts are Pareto optimal, and the incremental surplus generated in a principal-agent relationship accrues to the tenant. We design a simple non-cooperative game which implements the set of stable outcomes in subgame perfect equilibrium. We also suggest policy measures in relation to efficiency and income distribution.

It is shown that player mobility has important consequences for the long-run equilibrium distribution in dynamic evolutionary models of strategy adjustment, when updating is prone to small probability perturbations, i.e. “mistakes" or “mutations." Ellison (1993) concluded that the effect on the matching process of localized “neighborhoods" was to strengthen the stability of risk-dominant outcomes, originally demonstrated by Kandori, Mailath, and Rob (1993) (KMR) and Young (1993). I consider a model in which players can choose the neighborhoods to which they belong. When strategies and locations are updated simultaneously, only efficient strategies survive. The robustness of this conclusion is emphasized in a general locational model in which strategy revision opportunities are allowed to arrive at a faster rate than opportunities to change locations. The efficient strategy persists in all cases in which the locational structure is non-trivial. Moreover, even as the relative frequency of player mobility approaches zero, the efficient strategy occurs with boundedly positive relative frequency. This result is in stark contrast to the conclusions of the previous models.

This paper concerns the interpretation of equilibrium in non-additive beliefs in two-player normal form games. We argue that such equilibria involve beliefs and actions which are consistent with a lack of common knowledge of the game. Our argument rests on representation results which show that different notions of equilibrium in games with non-additive beliefs may be reinterpreted as equilibrium in associated games of incomplete information with additive (Bayesian) beliefs where common knowledge of the (original) game does not apply. The representation results show one way of comparing and understanding the various notions of equilibrium, for games with non-additive beliefs, advanced in the literature.

We analyze the subgame-perfect equilibria of a game where two agents bargain in order to share the risk in their assets that will pay dividends once at some fixed date. The uncertainty about the size of the dividends is resolved gradually by the payment date and each agent has his own view about how the uncertainty will be resolved. As agents become less uncertain about the dividends, some contracts become unacceptable to some party to such an extent that at the payment date no trade is possible. The set of contracts is assumed to be rich enough to generate all the Pareto-optimal allocations. We show that there exists a unique equilibrium allocation, and it is Pareto-optimal. Immediate agreement is always an equilibrium outcome; under certain conditions, we further show that in equilibrium there cannot be a delay. In this model, the equilibrium shares depend on how the uncertainty is resolved, and an agent can lose when his opponent becomes more risk-averse. Finally, we characterize the conditions under which every Pareto-optimal and individually rational allocation is obtainable via some bargaining procedure as the unique equilibrium outcome.

We present three examples of finitely repeated games with public monitoring that have sequential equilibria in private strategies, i.e., strategies that depend on own past actions as well as public signals. Such private sequential equilibria can have features quite unlike those of the more familiar perfect public equilibria: (i) making a public signal less informative can create Pareto superior equilibrium outcomes; (ii) the equilibrium final-period action profile need not be a stage game equilibrium; and (iii) even if the stage game has a unique correlated (and hence Nash) equilibrium, the first-period action profile need not be a stage game equilibrium.

This paper studies an incentive rationale for the use of group lending as a method of financing liquidity-constrained entrepreneurs. The joint liability feature associated with group lending lowers the liquidity risk of default but creates a free-riding problem. In the static setting, the free-riding problem dominates the liquidity risk effect under a plausible condition, thus making group lending unattractive. When the projects are repeated infinitely many times, however, the joint liability feature provides the group members with a credible means of exercising peer sanction, which can make the group lending attractive, relative to individual lending.

This paper provides an explanation for noisy pricing based on the strategic interaction of two firms competing in prices. When a firm adds noise to its prices, undercutting it becomes harder. Therefore, noisy pricing allows a firm to either exclude a competitor while charging supracompetitive prices, or to soften competition and have both firms earn supracompetitive profits. Such behavior leads to prices lying between competitive and monopolistic levels, and harms consumers and social welfare. It occurs in equilibrium if firms set prices sequentially, and in some equilibria of a repeated game of simultaneous price-setting if one firm is patient.

This paper studies the efficiency of collusion between supervisors and supervisees. Building on Tirole (1986)'s results that deterring collusion with infinitely risk averse supervisors is impossible, while it is costless to do so under risk neutrality, we develop here a theory of collusion based on a trade-off between the risk premia required by (less extreme) risk attitudes and incentives. This allows us to link the efficiency of collusion to the supervisor's risk aversion and to various parameters characterizing the economic environment in which collusion may take place. We are then able to derive implications for the design of organizations, like determining how the number of tasks/agents per supervisor or the level of competition may impact on the cost of collusion, studying the impact of vertical integration on those same costs, or characterizing the role of uncertainty on side-contracting.

This paper analyses the role of the managers' non-pecuniary private benefits in an incomplete contract approach to the regulation of utilities. Private benefits may take various forms: excessive job security, perks, overstaffing, feeling of power. The model describes the relationship between a government and the manager of a firm which produces a pure public good, under private or public ownership. The firm's production is characterized by its quantity and its flexibility, the latter corresponding to adaptability to changes in consumers' tastes or to new technologies. A larger output quantity entails larger private benefits to the manager, while increasing flexibility runs counter to the managers' private benefits. The manager decides upon non-verifiable investment in human and non-human capital so as to facilitate an increase in the output quantity (capacity investment) or to improve the firm's flexibility (investment in organizational adaptability). We compare the effects of the ownership regime on the manager's incentives to invest and on the aggregate welfare. The private firm under-invests in capacity and organizational flexibility. This is because the government holds up a part of the gains through ex post renegotiation of the initial (incomplete) contract. Our analysis also highlights a fundamental bias in the investment behavior of the state-owned firm: the manager of the public firm only invests in capacity (he may even invest more than under private ownership) but he never invests in organizational adaptability. The model shows that an increase in the government's bargaining power exacerbates the hold up problem when the firm is privately owned, but that this result may be reversed for capacity investment under public ownership. Finally, we show that the superiority of private or public ownership depends simultaneously on three factors: the respective bargaining power of the manager and of the government, the degree of specificity of investments and the relative weight of quantity and flexibility concerns in the social welfare.

Drawing insights from the literature and from the author's own survey work on contractual practices among manufacturers and traders in Africa, we study the transition from anonymous to personal to impersonal exchange. Using a dynamic game with heterogenous agents and information sharing, we derive precise conditions under which relational contracting spontaneously emerges and deters opportunistic breach even in the absence of formal market institutions. Exclusion of cheaters is not required for contracting to begin. As exchange develops, newcomers may be excluded from contracting when screening costs are high and agents long lived. Reputational equilibria in which cheaters are permanently excluded are not decentralizable unless contracting is already developed and breach of contract is interpreted as a sign of impending bankruptcy.

The bias of forward exchange rates as a predictor of future spot rates is typically explained or decomposed as (1) a risk premium and (2) a convexity term which accounts for the fact that, when there is stochastic inflation, nominal gains from forward currency speculation are higher than real ones and correspondingly losses are smaller. We use Nalebuff’s envelope puzzle to explain a third source of bias which involves real profits from foreign exchange speculation. Both the "real profit" bias and stochastic inflation bias arise from convexity of g(s)=1/s and so derive from Jensen's inequality as observed by Siegel (1972).

Bernardo and Ledoit (2000) develop a very appealing framework to compute pricing bounds based on what they call gain-loss ratio. Their method has many advantages and very interesting properties and so far one important drawback: the complexity of the numerical computation of the pricing bounds. In this note we provide a simple procedure for their computation which only entails solving a linear optimization program.