Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Cooperative production and efficiency

We characterize the sharing rule for which a contribution mechanism achieves efficiency in a cooperative production setting when agents are heterogeneous. The sharing rule bears no resemblance to those considered by the previous literature. We also show for a large class of sharing rules that if Nash equilibrium yields efficient allocations, the production function displays constant returns to scale, a case in which cooperation in production is useless.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

The Complete Information First. Price Auction or the Importance of Being Indivisible

Abstract Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the first-price sealed-bid auction mechanism under complete information. This paper aims to remedy that omission. We show that the existence of pure strategy undominated Nash equilibria requires that the bidding space is not "too divisible" (that is, a continuum). In fact, when bids must form part of a finite grid there always exists a "high price equilibrium". However, there might also be "low price equilibria" and when the bidding space is very restrictive the revenue obtained in these "low price equilibria" might be very low. We discuss the properties of the equilibria and an application of auction theoretical thinking in which "low price equilibria" may be relevant. Keywords: First-price auctions, undominated Nash equilibria. JEL Classification Numbers: C72 (Noncooperative Games), D44 (Auctions).

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

On Public Inefficiencies in a Mixed Duopoly

The aim of this paper is to investigate the welfare effect of a change in the public firms objective function in oligopoly when the government takes into account the distortionary effect of rising funds by taxation (shadow cost of public funds). We analyze the impact of a shift from welfare- to profit-maximizing behaviour of the public firm on the timing of competition by endogenizing the determination of simultaneous (Nash-Cournot) versus sequential (Stackelberg) games using the game with observable delay proposed by Hamilton and Slutsky (1990). Differently from previous work that assumed the timing of competition, we show that, absent efficiency gains, instructing the public firm to play as a private one never increases welfare. Moreover, even when large efficiency gains result from the shift in public firm's objective, an inefficient public firm that maximizes welfare may be preferred.

Subsidies as Optimal Fiscal Stimuli

In the theoretical macroeconomics literature, fiscal policy is almost uniformly taken to mean taxing and spending by a ‘benevolent government’ that exploits the potential aggregate demand externalities inherent in the imperfectly competitive nature of goods markets. Whilst shown to raise aggregate output and employment, these policies crowd-out private consumption and hence typically reduce welfare. In this paper we consider the use of ‘tax-and-subsidise’ instead of ‘taxand- spend’ policies on account of their widespread use by governments, even in the recent recession, to stimulate economic activity. Within a static general equilibrium macro-model with imperfectly competitive good markets we examine the effect of wage and output subsidies and show that, for a small open economy, positive tax and subsidy rates exist which maximise welfare, rendering no intervention as a suboptimal state. We also show that, within a two-country setting, a Nash non-cooperative symmetric equilibrium with positive tax and subsidy rates exists, and that cooperation between trading partners in setting these rates is more expansionary and leads to an improvement upon the non-cooperative solution.

Correlated equilibria, good and bad: an experimental study

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of the Nash equilibrium concept. Specifically, we seek to understand the conditions under which subjects playing the game of Chicken will condition their behavior on private, third–party recommendations drawn from known distributions. In a “good–recommendations” treatment, the distribution we use is a correlated equilibrium with payoffs better than any symmetric payoff in the convex hull of Nash equilibrium payoff vectors. In a “bad–recommendations” treatment, the distribution is a correlated equilibrium with payoffs worse than any Nash equilibrium payoff vector. In a “Nash–recommendations” treatment, the distribution is a convex combination of Nash equilibrium outcomes (which is also a correlated equilibrium), and in a fourth “very–good–recommendations” treatment, the distribution yields high payoffs, but is not a correlated equilibrium. We compare behavior in all of these treatments to the case where subjects do not receive recommendations. We find that when recommendations are not given to subjects, behavior is very close to mixed–strategy Nash equilibrium play. When recommendations are given, behavior does differ from mixed–strategy Nash equilibrium, with the nature of the differ- ences varying according to the treatment. Our main finding is that subjects will follow third–party recommendations only if those recommendations derive from a correlated equilibrium, and further, if that correlated equilibrium is payoff–enhancing relative to the available Nash equilibria.

Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot

In this paper, we consider an exchange economy µa la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably in¯nite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we par- tially replicate the mixed exchange economy by increasing the number of atoms, without a®ecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

The Impact of Information Provision on Agglomeration Bonus Performance: An Experimental Study on Local Networks

The Agglomeration Bonus (AB) is a mechanism to induce adjacent landowners to spatially coordinate their land use for the delivery of ecosystem services from farmland. This paper uses laboratory experiments to explore the performance of the AB in achieving the socially optimal land management configuration in a local network environment where the information available to subjects varies. The AB poses a coordination problem between two Nash equilibria: a Pareto dominant and a risk dominant equilibrium. The experiments indicate that if subjects are informed about both their direct and indirect neighbors’ actions, they are more likely to coordinate on the Pareto dominant equilibrium relative to the case where subjects have information about their direct neighbors’ action only. However, the extra information can only delay – and not prevent – the transition to the socially inferior risk dominant Nash equilibrium. In the long run, the AB mechanism may only be partially effective in enhancing delivery of ecosystem services on farming landscapes featuring local networks.

Dominance Solvable Games with Multiple Payoff Criteria.

Two logically distinct and permissive extensions of iterative weak dominance are introduced for games with possibly vector-valued payoffs. The first, iterative partial dominance, builds on an easy-to check condition but may lead to solutions that do not include any (generalized) Nash equilibria. However, the second and intuitively more demanding extension, iterative essential dominance, is shown to be an equilibrium refinement. The latter result includes Moulin’s (1979) classic theorem as a special case when all players’ payoffs are real-valued. Therefore, essential dominance solvability can be a useful solution concept for making sharper predictions in multicriteria games that feature a plethora of equilibria.

Atomic Cournotian Traders May Be Walrasian.

In a bilateral oligopoly, with large traders, represented as atoms, and small traders, represented by an atomless part, when is there a non-empty intersection between the sets of Walras and Cournot-Nash allocations? Using a two commodity version of the Shapley window model, we show that a necessary and sufficient condition for a Cournot- Nash allocation to be a Walras allocation is that all atoms demand a null amount of one of the two commodities. We provide two examples which show that this characterization holds non-vacuously. When our condition fails to hold, we also confirm, through some examples, the result obtained by Okuno, Postlewaite, and Roberts (1980): small traders always have a negligible influence on prices, while the large traders keep their strategic power even when their behavior turns out to be Walrasian in the cooperative framework considered by Gabszewicz and Mertens (1971) and Shitovitz (1973).

Keeping Up with the Joneses: Who Loses Out?

This paper investigates how well-being varies with individual wage rates when individuals care about relative consumption and so there are Veblen effects – Keeping up with the Joneses – leading individuals to over-work. In the case where individuals compare themselves with their peers – those with the same wage-rate - it is shown that Keeping up with the Joneses leads some individuals to work who otherwise would have chosen not to. Moreover for these individuals well-being is a decreasing function of the wage rate - contrary to standard theory. So those who are worst-off in society are no longer those on the lowest wage.

Consumption Decisions When People Value Conformity

In this paper we assume that for some commodities individuals may wish to adjust their levels of consumption from their normal Marshallian levels so as to match the consumption levels of a group of other individuals, in order to signal that they conform to the consumption norms of that group. Unlike Veblen’s concept of conspicuous consumption this can mean that some individuals may reduce their consumption of the relevant commodities. We model this as a three-stage game in which individuals first decide whether or not they wish to adhere to a norm, then decide which norm they wish to adhere to, and finally decide their actual consumption. We present a number of examples of the resulting equilibria, and then discuss the potential policy implications of this model.