Higher order game dynamics

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players? strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the players? evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics. We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n   orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n?2$n?2$. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg [7]. Finally, we also establish a higher order analogue of the folk theorem of evolutionary game theory, and we show that convergence to strict equilibria in n-th order dynamics is n orders as fast as in first order.     

Bounding the inefficiency of equilibria in nonatomic congestion games

Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a “best possible” outcome. We study a nonatomic version of the congestion games defined by Rosenthal [Int. J. Game Theory 2 (1973) 65], and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players—games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games.     

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.     

Unit Root Investigation of Greek Real Money Supply and GDP

In this article, the time series of Greek real GDP and real money supply are investigated for the presence of a unit root, allowing for maximum two breaks which take place at an unknown point in time. This methodology is preferred to conventional Dickey & Fuller tests because the covered time horizon, namely from 1858 to 1938, is characterized by a number of very important events, the nature of which is either economic or historical. In addition, time series stationarity is checked through a Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test.University of Macedonia—Greece. The article was presented at the Fifty-Ninth International Atlantic Economic Conference, London, England, March 9–13, 2005     

Estimating VARs with long stationary heterogeneous panels: A comparison of the fixed effect and the mean group estimators

The most promising candidates for estimating vector autoregressive models with long, stationary, possibly heterogeneous panel data sets (panel-VARs) are the fixed effect (FE) and the mean group (MG) estimators. With a view to providing guidance to applied researchers on how to pool in a panel-VAR, this paper compares the performance of the FE and the MG estimators both asymptotically and in Monte Carlo simulations. The main results of the analysis suggest the use of both estimators in applied work. If FE and MG estimates give similar estimates, the FE estimator should be used because it is more efficient. If they differ, the MG estimator should be used only if the panel is sufficiently long — say, twice as long as usually recommended in the dynamic panel data literature. If FE and MG estimates differ and the panel is not long enough, neither is generally a desirable alternative and other estimation techniques are needed.     

ON THE NEUTRALITY OF COALITION FORMATION IN A PURE BARGAINING PROBLEM*

We consider the sequential bargaining game à la Stahl–Binmore–Rubinstein with random proposers, juxtaposing an ex ante coalition formation stage to their bargaining game. On the basis of the expected outcomes in the negotiation over how to split a dollar, players can form coalitions in a sequential manner, within each of which they can redistribute their payoffs. It turns out that the grand coalition does form, and that each player receives his discounted expected payoff, which is obtained by playing as a single player in the negotiation, although there could be many equilibria in the bargaining stage.     

The computational complexity of random serial dictatorship

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assignment where indifferences are unavoidable. While executing RSD is obviously feasible, we show that computing the resulting probabilities is #P-complete, and thus intractable, both in the context of voting and assignment.     

Program equilibrium

In a computerized setting, players' strategies can be implemented by computer programs, to be executed on a shared computational devise. This situation becomes typical to new Internet economies, where agent technologies play a major role. This allows the definition of a program equilibrium. Following the fundamental ideas introduced by von Neumann in the 1940s (in parallel to his seminal contribution to game theory), a computer program can be used both as a set of instructions, as well as a file that can be read and compared with other files. We show that this idea implies that in a program equilibrium of the one-shot prisoners dilemma mutual cooperation is obtained. More generally, we show that the set of program equilibrium payoffs of a game coincides with the set of feasible and individually rational payoffs of it.     

On the Nash bargaining solution with noise

Suppose two parties have to share a surplus of random size. Each of the two can either commit to a demand prior to the realization of the surplus - as in the Nash demand game - or remain silent and wait until the surplus was observed. Adding the strategy to wait results in two strict equilibria, in each of which one player takes almost the whole surplus, provided uncertainty is small. If commitments concern only who makes the first offer, the more balanced Nash bargaining solution is approximately restored. In all cases, commitment occurs in equilibrium - despite the risk of breakdown of negotiations.     

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.     

Volatility spill-overs in commodity spot prices: New empirical results

The classical rational expectations model of commodity markets implies that expected spot price risk is an explanatory variable in spot price regressions; and also that inventory carryover, which is reduced by a larger price variance, creates autoregressive conditional heteroscedastic processes in spot prices. In order to falsify/verify this theory, it has typically been assumed that the square root of the conditional variance of spot prices, a proxy for spot price risk, enters the conditional mean function of spot prices. Based on this simple representation, a typical but counter intuitive outcome has been that spot price risk has an insignificant impact on spot prices, see, e.g., Beck (Beck, S., 1993. A Rational Expectations Model of Time Varying Risk Premia in Commodities Futures Markets: Theory and Evidence. International Economic Review 34, 149–168, Beck, S., 2001. Autoregressive Conditional Heteroskedasticity in Commodity Spot Prices. Journal of Applied Econometrics 16, 115–132). In this paper, we propose an alternative functional relationship (from GARCH(1,1) to GARCH(1,1)-AR(m)) between spot price risk and spot prices that is fully supported by the classical rational expectations model, and based on this new representation we are able to provide stronger empirical support for Muth's rational expectation theory.     

Clever agents in adaptive learning

Saez-Marti and Weibull (J. Econom. Theory 86 (1999) 268) investigate the consequences of letting some agents play a myopic best reply to the myopic best reply in Young's (J. Econom. Theory 59 (1993) 145) bargaining model, which is how they introduce “cleverness” of players. I analyze such clever agents in general finite two-player games and show Young's (Individual Strategy and Social Structure, Princeton University Press, Princeton, NJ, 1998) prediction to be robust: adaptive learning with clever agents does select the same minimal curb set as in the absence of clever agents, if their population share is less than one. However, the long-run strategy distribution in such a curb set may vary with the share of clever agents.     

An evolutionary approach to learning in a changing environment

The evolutionary fitness of the ability to learn a best response (at a cost) is explored in an environment where the underlying game changes stochastically over time. We provide a sufficient condition for asymptotic dominance by the learners. It does not require that the learners are the most fit type in any single state of the environment. We identify a necessary and sufficient condition that ensures the survival of the learners when learning costs are small. Last, we describe a medium-run phenomenon where the learners “spike”—their share temporarily rises and gets arbitrarily close to one following a regime shift.     

Randomization and simplification in dynamic decision-making

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision-maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in noninteractive deterministic environments where the decision-maker's choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components: an action selection rule and a behavior modification rule. In noninteractive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.     

The role of mediation in peacemaking and peacekeeping negotiations

We develop a model of bargaining that provides a rationale for the difference in the method of negotiation, depending on the nature of the conflict. We distinguish those negotiations that take place previous to a potential conflict (peacekeeping), and negotiations inside the conflict (peacemaking). In these contexts, we study the role of a mediator who tries to achieve a certain balance between the efficiency of the agreement and the equality of the final sharing. We show that the credibility of the mediator comes from her willingness to impose delays in the negotiation, even if that implies costs. We also find how the player with a “weak” bargaining position in a conflict can strategically profit from the mediator's quest for equality. Finally, we show how the capacity of the mediator to induce a higher equality in the sharing is always higher in a peacemaking situation than in a peacekeeping one.     

Estimating aggregate autoregressive processes when only macro data are available

The aggregation of individual random AR(1) models generally leads to an AR(∞$\infty$) process. We provide two consistent estimators of aggregate dynamics based on either a parametric regression or a minimum distance approach for use when only macro data are available. Notably, both estimators allow us to recover some moments of the cross-sectional distribution of the autoregressive parameter. Both estimators perform very well in our Monte-Carlo experiment, even with finite samples.     

Self-tuning experience weighted attraction learning in games

Self-tuning experience weighted attraction (EWA) is a one-parameter theory of learning in games. It addresses a criticism that an earlier model (EWA) has too many parameters, by fixing some parameters at plausible values and replacing others with functions of experience so that they no longer need to be estimated. Consequently, it is econometrically simpler than the popular weighted fictitious play and reinforcement learning models. The functions of experience which replace free parameters “self-tune” over time, adjusting in a way that selects a sensible learning rule to capture subjects’ choice dynamics. For instance, the self-tuning EWA model can turn from a weighted fictitious play into an averaging reinforcement learning as subjects equilibrate and learn to ignore inferior foregone payoffs. The theory was tested on seven different games, and compared to the earlier parametric EWA model and a one-parameter stochastic equilibrium theory (QRE). Self-tuning EWA does as well as EWA in predicting behavior in new games, even though it has fewer parameters, and fits reliably better than the QRE equilibrium benchmark.     

Estimating semi-parametric output distance functions with neural-based reduced form equations using LIML

Efficiency analysis is an important tool for evaluating firms' performance. This paper introduces a novel approach for measuring technical efficiency (TE) in the case of technologies with multiple outputs which deals with the endogeneity of outputs issue. The proposed approach uses Artificial Neural Networks (ANNs) and the method of Limited Information Maximum Likelihood (LIML). The validity of the proposed approach is illustrated by fitting it to a large US data set for all commercial banks in the 1989–2000 time span. Meanwhile, we compare the proposed approach to the single-equation Translog output distance function and the proposed approach was found to yield very satisfactory results, while dealing with the issue of the endogeneity of outputs.     

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.