Pre-play communication with forgone costly messages: experimental evidence on forward induction

We experimentally study optional costly communication in Stag-Hunt games. Prior research demonstrates that efficient coordination is difficult without a communication option but obtains regularly with mandatory costless pre-play messages. We find that even small communication costs dramatically reduce message use when communication is optional, but efficient coordination can occur with similar frequency as under costless communication. These findings can be accounted for by formalizations of forward induction that take Nash equilibrium as a reference point (such as Kohlberg and Mertens in Econometrica 54: 1003–1037, 1986; Govindan and Wilson in Econometrica 77: 1–28, 2009), while formalizations that only appeal to (higher-order) knowledge of rationality remain silent in this environment.     

On the Generic Finiteness of Equilibrium Outcomes in Plurality Games

In this paper we prove that for generic (noncooperative) voting games under plurality rule the set of equilibria that induce a mixed distribution over the outcomes (i.e., with two or more candidates elected with positive probability) is finite and, furthermore, each of these equilibria is regular. From that we deduce the finiteness of the set of equilibrium distributions over outcomes. Furthermore we offer an example (S. Govindan and A. McLennan, 1997, “On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms,” mimeo) that shows the impossibility of extending such results to a general framework, even just to voting games. Journal of Economic Literature Classification Numbers: C72, D72.     

What is an ‘endogenous state space’?

Summary. In the literature on choice under unforeseen contingencies, the decision maker behaves as if she aggregates possible instances of future rankings indexed by a set S. The set S is interpreted as a subjective state space even though subsequent rankings need not conform to any one of the aggregated utilities. This paper proposes a definition for a subjective state space under unforeseen contingencies that is topologically unique, derives its existence from preference primitives as opposed to the representation of preferences, and does not commit to an interpretation in which states correspond to future realized rankings. The definition topologically concurs with and extends the identification of the essentially unique subjective state space due to Dekel, Lipman and Rustichini [4].Received: 28 October 2003, Revised: 13 October 2004, JEL Classification Numbers: D11, D81, D91.I thank Eddie Dekel, Alan Kraus, Bart Lipman, Chris Shannon, and the referee for some helpful remarks.     

Equilibrium tracing in strategic-form games

We analyze the relationships of the van den Elzen–Talman algorithm, the Lemke–Howson algorithm and the global Newton method for equilibrium computation by Govindan and Wilson. For two-player games, all three can be implemented as complementary pivoting algorithms. The algorithms by Lemke and Howson and by van den Elzen and Talman start at a pair of strategies: the first method at a pure strategy and its best reply, the latter anywhere in the strategy space. However, we show that even with the same starting point they may find different equilibria. Our second result is that the van den Elzen–Talman algorithm is a special case of the global Newton method, which was known only for the Lemke–Howson algorithm. More generally, the global Newton method implements the linear tracing procedure for any number of players. All three algorithms find generically only equilibria of positive index. Even though the van den Elzen–Talman algorithm is extremely flexible in the choice of starting point, we show that there are generic coordination games where the completely mixed equilibrium, which has positive index, is generically not found by the algorithm.     

Spanning,valuation and options

Summary We model the space of marketed assets as a Riesz space of commoditics. In this setting two altenative characterizations are given of the space of continuous options on a bounded asset,s, with limited liability. The first characterization represents every continuous option ons as the uniform limit of portfolios of calls ons. The second characterization represents an option as a continuous sum (or integral) of Arrow-Debreu securities, with respect tos. The pricing implications of these representations are explored. In particular, the Breeden-Littzenberger pricing formula is shown to be a direct consequence of the integral representation theorem.Research supported in part by NSF Grant SES83-19611     

Strategic Rationality Orderings and the Best Rationalization Principle

In a finite game fix a space of extended probabilities over strategies and a profile of best response correspondences. A profile ofrationality orderingsis then given by an ordered partition of the set of strategies of each player, representing different degrees of rationality, where at-leastk+1-rational strategies are best responses against extended probabilities reflecting at leastkdegrees of rationality. This solution can be constructed inductively, providing a Bayesian foundation for controversial deletion procedures such as extensive form rationalizability and iterated weak dominance. Focusing on extensive games, this approach formalizes the best rationalization principle.Journal of Economic LiteratureClassification Number: C72.     

Benchmarking real-valued acts

A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional V(f)=P(fβ). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P.     

The Organization of Production and its Publics: Mental Proximity,Market and Hierarchies

The paper introduces mental proximity as an ideal-type criterion for assessing the organization of production, and positions it as a benchmark alongside markets and hierarchies in a three-dimensional space. Following a Deweyan approach, the criterion is focused on democratic deliberation espoused by necessary values: the rejection of controlling influences, positive freedom, inclusion on equal terms, informed participation, the desire to reach a consensus, sympathy, mutual respect, reciprocity, and continuous learning. We also identify a community network as a complex of people who seek to relate to each other in accord with mental proximity, and discuss influences on their search.     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Aggregation of semiorders: intransitive indifference makes a difference

Summary A semiorder can be thought of as a binary relationP for which there is a utilityu representing it in the following sense:xPy iffu(x) –u(y) > 1. We argue that weak orders (for which indifference is transitive) can not be considered a successful approximation of semiorders; for instance, a utility function representing a semiorder in the manner mentioned above is almost unique, i.e. cardinal and not only ordinal. In this paper we deal with semiorders on a product space and their relation to given semiorders on the original spaces. Following the intuition of Rubinstein we find surprising results: with the appropriate framework, it turns out that a Savage-type expected utility requires significantly weaker axioms than it does in the context of weak orders.We wish to thank Tatsuro Ichiishi, Jorge Nieto, Ariel Rubinstein, Efraim Sadka and especially David Schmeidler and anonymous referees for stimulating discussions and comments. I. Gilboa received partial financial support from NSF grants nos. IRI-8814672 and SES-9113108, as well as from the Alfred P. Sloan Foundation.     

A general structure theorem for the Nash equilibrium correspondence

I consider n-person normal form games where the strategy set of each player is a non-empty compact convex subset of an Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in the player i's strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. I demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well-known structure theorem in [Kohlberg, E., Mertens, J.-F., 1986. On the strategic stability of equilibria. Econometrica 54, 1003–1037]. It is supplemented by an extension analogous to the unknottedness theorems in [Demichelis S., Germano, F., 2000. Some consequences of the unknottedness of the Walras correspondence. J. Math. Econ. 34, 537–545; Demichelis S., Germano, F., 2002. On (un)knots and dynamics in games. Games Econ. Behav. 41, 46–60]: the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games.     

Benefit and Distance Functions

We explore the relationship between R. W. Shephard's input distance function (“Cost and Production Functions,” Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ.21(1992a), 461–481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in both price and input space. D. McFadden's (Cost, revenue, and profit functions,in“Production Economics: A Dual Approach to Theory and Applications, “North-Holland/Elsevier, New York, 1978) composition rules for input sets and input distance functions are then extended to the directional input distance function.Journal of Economic LiteratureClassification Numbers : D21, D24, D29.     

New market creation through transformation

Is new market creation a search and selectionprocess within the theoretical space of all possible markets? Or is it the outcome of a process of transformation of extant realities into new possibilities? In this article we consider new market creation as a process involving a new network of stakeholders. The network is initiated through an effectual commitment that sets in motion two concurrent cycles of expanding resources and convergingconstraints that result in the new market. The dynamic model was induced from two empirical investigations, a cognitive science-based investigation of entrepreneurial expertise, and a real time history of the RFID industry. JEL Classification: M13, M31, D4, D52, D71, D72, L1, L2, P42 We would like to thank the Batten Institute at the Darden Graduate School of Business Administration, University of Virginia, for supporting this research. We would also like to thank the following on specific contributions to our thesis: Anil Menon for his relentless insistence on more precise formulations of effectual reasoning; Jim March for his conversation and for inspiring us to dig into Type I and Type II errors; Rob Wiltbank for firming up the section on opportunity costs; and Stuart Read for helping us clarify our writing. Correspondence to: S.D. Sarasvathy     

Communication, Risk, and Efficiency in Games

This paper uses curb sets to study the evolution of effective pre-play communication in games where a single communication round precedes a simultaneous-move, complete-information game. It is shown that the effectiveness of one-sided pre-play communication is inversely related to risk in the underlying game, and to the size of the message space. If messages have somea prioriinformation content, then multi-sided communication is more effective than one-sided communication; i.e., risk and the size of the message space play no role.Journal of Economic LiteratureClassification Number: C72.     

A Characterization of Ordinal Potential Games

This note characterizes ordinal potential games by the absence of weak improvement cycles and an order condition on the strategy space. This order condition is automatically satisfied if the strategy space is countable.Journal of Economic LiteratureClassification Number: C72.     

Preference for flexibility in infinite horizon problems

Summary. We consider the extension of the classical problem of preference for flexibility to many periods. Preferences are defined over sets of infinite paths of choices. The main result provides a set of axioms on preferences that yield an additive representation over a subjective state space. This space is the set of preferences over choice today and feasible set tomorrow. The main new axiom, stochastic dominance, is a stronger form of the assumption of monotonicity. Received: September 11 2000; revised version: December 18, 2001     

Geopolitics and the Screen: War,the Body and Violence

The paper investigates the promise of Carl Schmitt's concept of ‘nomos’ for developing new spatial imaginaries apposite to the study of ‘the border’ in contemporary political life, as per the aims of the ‘Lines in the Sand’ research agenda. Schmitt introduced the idea of a ‘nomos of the earth’ to refer to the fundamental relation between space and political order. There have been various historical expressions of the nomos, from the Respublica Christiana, to the jus publicum Europaeum, to a post–World War II (dis)order yet to be adequately theorised. We aim to explore the relatively overlooked spatial ontology of Schmitt's work and suggest ways in which it might prompt alternative ways of thinking about borders and bordering practices as representative of broader dynamics in the relation between space and political order.     

A representation theorem for Riesz spaces and its applications to economics

Summary We show that a Dedekind complete Riesz space which contains a weak unite and admits a strictly positive order continuous linear functional can be represented as a subspace of the spaceL ₁ of integrable functions on a probability measure space in such a way that the order ideal generated bye is carried ontoL _t8. As a consequence, we obtain a characterization of abstractM-spaces that are isomorphic to concreteL -spaces. Although these results are implicit in the literature on representation of Riesz spaces, they are not available in this form. This research is motivated by, and has applications in, general equilibrium theory in infinite dimensional spaces.We thank Robert Anderson and Neil Gretsky for several useful conversations. The third author also gratefully acknowledges financial support from the Deutscheforschungsgemeinschaft, Gottfried Wilhelm Leibniz Forder preis, the National Science Foundation, and the UCLA Academic Senate Committee on Research.     

Non-well-founded-Type Spaces

In a Harsanyi-types space, states become circular, self-referring objects if one tries to make the types an explicit part of the states' structure. To make such a definition rigorous, we suggest the use ofnon-well-founded setsthat may be members of themselves, members of their members, etc. We show how to define the non-well-founded version of a types space in a way that preserves nature and the mutual uncertainties. This non-well-founded version is isomorphic to a beliefs subspace of the Mertens–Zamir hierarchic construction, although its definition involves no inductive process.Journal of Economic LiteratureClassification Number: D82.