Fictitious play property of the Nash demand game

We show that the Nash demand game has the fictitious play property. We also show that almost every fictitious play process and its associated belief path converge to a pure-strategy Nash equilibrium in the Nash demand game.     

Structural estimation of congestion costs

We estimate a structural model of congestion costs using a Bayesian Nash equilibrium approach: The individual's preference for traveling depends on the anticipated level of congestion, which in turn is determined by travelers’ decisions of mobility. The model is estimated using a French transportation household survey. Results confirm the presence of incomplete information and show that aversion to congestion is 6.6% lower during peak times than during off-peak times. A traveler's willingness-to-pay to save 1 min in traffic is estimated at 0.73 euros during peak times and 0.25 euros during off-peak times.     

English auctions with resale: An experimental study

I design and test a simple English auction and two English auctions with resale, but with different informational backgrounds. All three treatments theoretically have the same equilibrium. I find, however, that the possibility of resale alters behavior significantly. In the two treatments with resale, subjects deviated from both the Nash prediction and the common results about bidding behavior in English auctions. Subjects tend to overbid, when they are certain they can reap the whole surplus in the resale market. I employ different models like QRE and levels of reasoning and conclude that overbidding can be explained as a rational response to the noisy environment in markets with human participants, that is, as rational decision making when anticipating others to make errors. When the outcome of the resale market is not certain, there is significant signaling behavior and auction prices tend to be lower than the Nash prediction.     

Implementation of college admission rules

Summary We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the lower bound stable rule is implementable in both senses. The upper bound Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments.     

Variational convergence: Approximation and existence of equilibria in discontinuous games

We introduce a notion of variational convergence for sequences of games and we show that the Nash equilibrium map is upper semi-continuous with respect to variationally converging sequences. We then show that for a game G with discontinuous payoff, some of the most important existence results of Dasgupta and Maskin, Simon, and Reny are based on constructing approximating sequences of games that variationally converge to G. In fact, this notion of convergence will help simplify these results and make their proofs more transparent. Finally, we use our notion of convergence to establish the existence of a Nash equilibrium for Bertrand-Edgeworth games with very general forms of tie-breaking and residual demand rules.     

Bargaining with revoking costs

A simple two stage bilateral bargaining game is analyzed. The players simultaneously demand shares of a unit size pie. If the demands add up to more than one, the players simultaneously choose whether to stick to their demand or accept the other?s offer. While both parties sticking to their offers leads to an impasse, accepting a lower share than the original demand is costly for each party. The set of pure strategy subgame perfect equilibria of the game is characterized for continuously differentiable payoff and cost functions, strictly increasing in the pie share and the amount conceded, respectively. Higher cost functions are shown to improve bargaining power. The limit equilibrium prediction of the model, as the cost functions are made arbitrarily high, selects a unique equilibrium in the Nash Demand Game that corresponds to a Proportional Bargaining Solution of Kalai (1977).     

Search theory,competitive equilibrium,and the Nash bargaining solution

We investigate a canonical search-theoretic model without entry. Two agents are randomly matched with a long side being rationed. The matched agents face a pair of randomly drawn non-transferable payoffs, and then choose whether or not to form a partnership subject to a small probability of exogenous break down. As this probability and friction vanish, the Nash bargaining solution emerges as the unique undominated strategy equilibrium outcome if the mass of each party is the same. If the size of one party is larger than the other, the short side extracts the entire surplus, a sharp contrast to Rubinstein and Wolinsky (1985) [16].     

R&D games in a Cournot duopoly with isoelastic demand functions: A comment

In a recent paper, Tramontana (Economic Modelling, 27; 350-357, 2010) investigates the stability properties of a Cournot Duopoly game when the demand function is isoelastic. In this note, we show that for some well known applications of two-stage Cournot games (D. Aspremont and Jacquemin, American Economic Review, 78, 1122-1137, 1988) an isoelastic demand function can guarantee both the existence and the uniqueness of a Nash Equilibrium even in cases where existence is not obtained with linear demands.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Optimal trade policy in tariff games with inside money

We construct a bilateral trade model incorporating two physical goods and a financial asset (inside money) to discuss the optimal trade policy that countries would choose to maximize their respective utilities. In this Nash tariff game, the trade of physical commodities only occurs geographically across countries, and the trade of inside money allows for intertemporal allocation of consumptions. When the preferences, present and future endowments for each country are given, according to our numerical analysis, trade surplus or deficit (inside money) and optimal tariff rates are endogenously determined when general equilibrium conditions hold. One country may purchase inside money to shift current consumption to the future, and the other may be willing to issue inside money for smoothing its consumptions in two periods. This imbalance trade contradicts traditional trade models which imply a balanced trade policy. We further find that the price of inside money as an implied interest rate also is determined by the trade intervention policies.     

Testing the TASP: An experimental investigation of learning in games with unstable equilibria

We report experiments studying mixed strategy Nash equilibria that are theoretically stable or unstable under learning. The Time Average Shapley Polygon (TASP) predicts behavior in the unstable case. We study two versions of Rock-Paper-Scissors that include a fourth strategy, Dumb. The unique Nash equilibrium is identical in the two games, but the predicted frequency of Dumb is much higher in the game where the NE is stable. Consistent with TASP, the observed frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment. However, Dumb is played too frequently in all treatments.     

Alternative unit root testing strategies using the Fourier approximation

Two alternatives to  and  Fourier unit root testing strategy, which incorporates pretesting for nonlinearity, are considered. One is based on the union of rejection (UR) approach, and the other is a hybrid strategy that combines the UR approach with the use of extra information from nonlinearity pretesting. Simulation results show that the two proposed strategies, especially the hybrid, frequently outperform the original pretesting strategy.     

Efficiency and surplus bounds in Cournot competition

We derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under Cournot competition. To do so, we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of ρ-concavity and ρ-convexity. The “more concave” is demand, the larger the share of producer surplus in overall surplus, the smaller is consumer surplus relative to producer surplus, and the lower the ratio of deadweight loss to producer surplus. Deadweight loss over total potential surplus is at first increasing with demand concavity, then eventually decreasing.     

The supercore for normal-form games

This paper analyzes the supercore of a system derived from a normal-form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore coincides with the set of Nash equilibria of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner's dilemma. With regard to the mixed extension of a normal-form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria.     

Out-of-equilibrium performance of three Lindahl mechanisms: Experimental evidence

We describe an experimental comparison of the out-of-equilibrium performance of three allocation mechanisms designed to achieve Lindahl outcomes as Nash equilibria: the mechanisms due to Walker (1981), Kim (1993), and Chen (2002). We find that Chen?s mechanism, which is supermodular, converges closest and most rapidly to its equilibrium. However, we find that the properties that move subjects toward equilibrium in Chen?s mechanism typically generate sizeable taxes and subsidies when not in equilibrium, and correspondingly large budget surpluses and deficits, which typically far outweigh the surplus created by providing the public good. The Kim mechanism, on the other hand, converges relatively close to its equilibrium and exhibits much better out-of-equilibrium efficiency properties.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Structural models, information and inherited restrictions

The derived structural estimates of the system βY = γZ + δU impose identifying restrictions on the reduced form estimates ex post. Some or all of the derived structural estimates are presented as evidence of the model's efficacy. In fact, the reduced form inherits a great deal of information from the structure's restrictions and hypothesized sign patterns, limiting the allowable signs for the reduced form. A method for measuring a structural model's statistical information content is proposed. Further, the paper develops a method for enumerating the allowable reduced form outcomes which can be used to falsify the proposed model independently of significant coefficients found for the structural relations.     

A review of experience curve analyses for energy demand technologies

Transitioning towards a sustainable energy system requires the large-scale introduction of novel energy demand and supply technologies. Such novel technologies are often expensive at the point of their market introduction but eventually become cheaper due to technological learning. In order to quantify potentials for price and cost decline, the experience curve approach has been extensively applied to renewable and non-renewable energy supply technologies. However, its application to energy demand technologies is far less frequent. Here, we provide the first comprehensive review of experience curve analyses for energy demand technologies. We find a widespread trend towards declining prices and costs at an average learning rate of 18 ± 9%. This finding is consistent with the results for energy supply technologies and for manufacturing in general. Learning rates for individual energy demand technologies are symmetrically distributed around the arithmetic mean of the data sample. Absolute variation of learning rates within individual technology clusters of 7 ± 4%-points and between technology clusters of 7 ± 5%-points both contribute to the overall variability of learning rates. Our results show that technological learning is as important for energy demand technologies as it is for energy supply technologies. Applying the experience curve approach to forecast technology costs involves, however, unresolved uncertainties, as we demonstrate in a case study for the micro-cogeneration technology.     

Giving gifts to groups: How altruism depends on the number of recipients

When a single gift goes to a group of recipients, how does giving depend on the size of the group? This question is important for understanding charitable giving and fund-raising, public goods provision, family altruism, and more. If we think of the gift as giving up a dollar to create a social surplus, then we want to know how the number of recipients of that surplus affects its value to the giver. In other words, how congestible is altruism? This paper builds a theoretical framework for this question and begins to answer it with a controlled experiment. The finding is that for most subjects altruism is congestible. For the average subject, a gift that results in one person receiving x is equivalent to one in which n people receive x / n^0.68 each.     

Structural holes in social networks

We consider a setting where every pair of players that undertake a transaction (e.g. exchange goods or information) creates a unit surplus. A transaction can take place only if the players involved have a connection. If the connection is direct the two players split the surplus equally, while if it is indirect then intermediate players also get an equal share of the surplus. Thus, individuals form links with others to create surplus, to gain intermediation rents, and to circumvent others who are trying to become intermediary.Our analysis clarifies the interplay between these forces in the process of strategic network formation. First, we show that, in the absence of capacity constraints on links, it leads to the emergence of a star network where a single agent acts as an intermediary for all transactions and enjoys significantly higher payoffs. Second, we study the implications of capacity constraints in the ability of agents to form links. In this case, distances between players must be long, which induces players who are “far off” to connect in order to avoid paying large intermediation rents. A cycle network then emerges, payoffs being equal across all players.