We examine the force of three types of behavioral dynamics in quantity-setting triopoly experiments: (1) mimicking the successful firm, (2) rules based on following the exemplary firm, and (3) rules based on belief learning. Theoretically, these three types of rules lead to the competitive, the collusive, and the CournotNash outcome, respectively. In the experiment we employ three information treatments, each of which is hypothesized to be conducive to the force of one of the three dynamic rules. To a large extent, the results are consistent with the hypothesized relationships between treatments, behavioral rules, and outcomes.

Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.

We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals. We show that to investigate the existence of such strongly stable networks one can restrict focus on a component-wise egalitarian allocation of value. We show that when such strongly stable networks exist they coincide with the set of efficient networks (those maximizing the total productive value). We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist strongly stable networks via a "top convexity" condition on the value function on networks. We also consider a variation on strong stability where players can make side payments, and examine situations where value functions may be non-anonymous-depending on player labels.

this paper I argue that neither of these solutions is necessary because the premises on which they are based are false. With a few specific exceptions, ethnic diversity neither increases the risk of civil war, nor reduces economic growth. Multi-ethnic societies can usually be socially and economically fully viable. In Section 2 I set out the current state of knowledge: what is meant by ethnic identity, and why is it thought to be dysfunctional? In Sections 3 and 4 I venture beyond the literature. In Section 3 I investigate how ethnic politics might affect economic performance, deriving predictions from theories of political choice and testing them on global data. In Section 4 I turn to the causes of large scale violence. I investigate how ethnic differentiation might effect civil conflict. Building on new theories of conflict which stress the importance of the budget constraint faced by the rebel organisation, I test three predictions on global data. In Section 5 I draw out some implications for policy. Ethnic diversity is not `guilty as charged. It does not, usually, cause slower growth, and it does not, usually, cause civil war. The international community may need to rethink its current tolerant approach to secession. 2. WHAT DO WE KNOW AND WHAT ARE THE GAPS? How does ethnicity sometimes come to be the basis for social and political identity? Ethnicity as a basis for identity is a social rather than a physiological phenomenon. As a cultural phenomenon ethnicity is nevertheless, highly persistent: people chose to pass on their culture by marrying within their own group (Bisin and Verdier, 2000). However, as a political phenomenon, ethnic identity is considerably more fluid. This is indeed implied by `national building in Europe perceptions of identity changed during t...

Economists model economic activity based on fairly standard assumptions about human behavior and decision making. The rationality assumption, in which all economic agents optimize well-defined objectives under complete information, has been the prevalent model in economics since its inception. Optimization formulations also arise in modeling market structures other than perfect competition and in games of strategic interaction. This sets up a close association between models in microeconomics, game theory, and industrial organization on the one hand, and mathematical programming, optimization, and complementarity theory on the other. Many mathematical programming solution techniques are applicable to the formulation and solution of economics models. This talk provides a brief overview of the connections between economics and mathematical programming / equilibrium modeling.

In a di#erential information economy ith quasi-linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints: the associated ex ante core is generically non-empty. Ho ever, e exhibit a ellbehaved exchange economy in hich this core is empty, even if goods are allocated through random mechanisms. THE EX ANTE INCENTIVE COMPATIBLE CORE IN THE ABSENCE OF WEALTH EFFECTS # FRAN COISE FORGE + , JEluq RAN COISME TEu # , AND RAJIV VOHRA 2000 MathematicsS ubject Classification. 91A12, 91B44, 91B60 JE Classification numbers. C71, D82, D51. Key words and phrases. Core, exchange economy, asymmetric information, incentive compatibility, ex ante, transferable utility, absence of wealth e#ects, quasi-linear. URL: ftp://jfm.core.ucl.ac.be/pub/papers/ICCore.ps.gz http://econ.pstc.brown.edu/~rvohra/papers/wp2001-01.pdf. # We wish t thankE nric Minelli f r numer us, extremely useful discussi ns n the t pic f this research. Als c nversati ns with Claude d'Asprem nt, Andy P stlewaite, R y Radner, Debraj Ray and R bert Serran have been very helpful. Financial supp rt fr mE ur pean TMR Netw rk FMRX CT 960055 and fr m a Sal m n research grant, Br wn University, is gratefully ackn wledged, as well as fr m the Belgian Pr gramme n Interuniversity P les f Attracti n, initiated by the Belgian State, Prime Minister's O#ce. +THEud Universite de Cergy-P nt ise, et Institut Universitaire de France. E-mail: forges@u-cergy.fr. #CORE Universite Cath lique de L uvain; 34, V ie du R man-Pays; B-1348 L uvain-la-Neuve; Belgique. E-mail: jfm@core.ucl.ac.be. Br wn University, Pr vidence, R.I. 02912, U.S.A. E-mail: Rajiv_Vohra@brown.edu. THE INCENTIVE COMPATIBLE CORE 1 1.

A solution to bargaining problems is ordinal when it is covariant with order-preserving transformations of utility. Shapley (1969) has shown that there exists no ordinal, e#cient, and symmetric solution to twoplayer bargaining problems, and has constructed such a solution to threeplayer problems. Here, Shapley's solution is extended in two directions. First, it is shown how to construct an infinite family of such solutions that includes Shapley's. Second, the family of solutions is constructed for bargaining problems with any number of players greater than two. The construction makes use of gradual bargaining solutions suggested by O'Neill et al. (2001). 1

Utility theories for the denitions of cooperative games and associated solution concepts are discussed. A game with side payments needs the assumptions of transferable utility and side payments. We discuss the axioms for the transferable utility assumption and also the role of side payments for various solution concepts. We also discuss games without side payments, which do not require the assumptions of transferable utility and side payments. We see how some solution concepts depend upon these assumptions.

world view obtained is highly different. In particular the four most important distinctions are: 1 Those who wish to delve further into details will find the three volume handbook editied by Aumann and Hart (1992, 1994 and 1997 forthcoming) to be of considerable assistance. 2 1. Game theory as mathematics; 2. Game theory as science; 3. Game theory as philosophy; 4. Game theory as advocacy. Some brief observations are made here on these distinctions. They will be expanded further in a subsequent note. After these are discussed, some basic exposition is given. 1. Game theory as mathematics Prior to the theory of games the prime emphasis in mathematical techniques applied to economics was to differential calculus, differential and difference equations. Combinatorics was hardly considered. The stress in von Neumann and Morgenstern was on choices among finite sets 2 . Not only did they stress finite combinatorics in individual c

this paper. The reader interested in this novel approach to social stability should consult either von Neumann and Morgenstern (1944) directly or Lucas (1992) 6 counterexamples to apparently reasonable conjectures, which can be established only in high dimensions. The stable set solution generated considerable mathematical investigation (as is indicated by the Lucas 1992 survey). However, to some extent due to its lack of universal existence, it has not been utilized much in applied game theory. Other cooperative solutions The most utilized cooperative solutions in the development of cooperative game theory have been the core and the value. They have been described in Part I; lesser known, but with a substantial literature are the bargaining set, the kernel and the nucleolus of a game. Intuitively the core reflects the imputations protected from the direct bargaining power of subgroups in a society (it reflects the limitations of countervailing power), the nucleolus is an imputation that has the property that the largest complaint against it by any group is minimized and the bargaining set and kernel reflect plausible requirements for an acceptable bargaining outcome. All of these solutions have lead to considerable mathematical investigation. A survey of the literatures on the bargaining set, kernel and nucleolus which covers, not only the mathematics, but indicates applications and gaming experiments has been provided by Maschler (1992) Noncooperative solutions The noncooperative equilibrium The ruling solution concept for games in strategic form is the noncooperative equilibrium of Nash (1950). A fixed point argument was utilized to show that for a finite matrix game there was an outcome which satisfied mutually consistent expectations. Unfortunately there may be m...