Mark A Walker

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Courses

Scholarly Contributions

Chapters

• Walker, M. A., & Wooders, J. (2008). Mixed Strategy Equilibrium. In The New Palgrave Dictionary of Economics(pp 628-631). Macmillan.
• Walker, M., & Moreno, D. (1995). Convergence Theorems for a Class of Recursive Stochastic Algorithms. In Economics of Decentralization: Complexity, Efficiency, and Stability. Kluwer Academic Press.
• Walker, M., & Muench, T. (1979). Identifying the Free Rider Problem. In Aggregation and Rvelation of Preferences(pp 61-87). North-Holland.

Journals/Publications

• Walker, M. A., & Van Essen, M. (2017). Simple Market-Like Allocation Mechanism for Public Goods. Games and Economic Behavior-Written version.
• Walker, M., & Van Essen, M. (2017). A Simple Market-Like Resource Allocation Mechanism. Games and Economic Behavior-Online.
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  Published online 2016.
• Essen, M. V., Lazzati, N., & Walker, M. (2012). Out-of-equilibrium performance of three Lindahl mechanisms: Experimental evidence. Games and Economic Behavior, 74(1), 366-381.
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  Abstract: 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. © 2011 Elsevier Inc.
• Garratt, R. J., Walker, M., & Wooders, J. (2012). Behavior in second-price auctions by highly experienced eBay buyers and sellers. Experimental Economics, 15(1), 44-57.
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  Abstract: We report on sealed-bid second-price auctions that we conducted on the Internet using subjects with substantial prior experience: they were highly experienced participants in eBay auctions. Unlike the novice bidders in previous (laboratory) experiments, the experienced bidders exhibited no greater tendency to overbid than to underbid. However, even subjects with substantial prior experience tended not to bid their values, suggesting that the non-optimal bidding of novice subjects is robust to substantial experience in non-experimental auctions. We found that auction revenue was not significantly different from the expected revenue the auction would generate if bidders bid their values. Auction efficiency, as measured by the percentage of surplus captured, was substantially lower in our SPAs than in previous laboratory experiments. © 2011 Economic Science Association.
• Walker, M., Wooders, J., & Amir, R. (2011). Equilibrium play in matches: Binary Markov games. Games and Economic Behavior, 71(2), 487-502.
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  Abstract: We study two-person extensive form games, or "matches," in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in "point games." We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided. © 2010 Elsevier Inc.
• Swarthout, J. T., & Walker, M. (2009). Discrete implementation of the Groves-Ledyard mechanism. Review of Economic Design, 13(1-2), 101-114.
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  Abstract: When implementing an economic institution in the field or in the laboratory, the participants' action spaces and the institution's outcomes are typically discrete, while our theoretical analysis of the institution often assumes the sets are continuous. Predictions by the continuous model generally turn out to be good approximations to the performance of the discrete implementation. We present an example in which the continuous version has a unique and Pareto efficient equilibrium, but in which the discrete version often has vastly more equilibria, many of them far from efficient. We show that the same phenomenon appears in two experiments investigating the Groves-Ledyard mechanism, and that it may account for the experimental results. © 2008 Springer-Verlag.
• Reiley, D. H., Urbancic, M. B., & Walker, M. (2008). Stripped-down poker: A classroom game with signaling and bluffing. Journal of Economic Education, 39(4), 323-341.
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  Abstract: The authors present a simplified, "stripped-down" version of poker as an instructional classroom game. Although Stripped-Down Poker is extremely simple, it nevertheless provides an excellent illustration of a number of topics: signaling, bluffing, mixed strategies, the value of information, and Bayes's Rule. The authors begin with a description of Stripped-Down Poker: how to play it, what makes it an interesting classroom game, and how to teach its solution to students. They describe how signaling, bluffing, and so forth emerge naturally as important features of the game and then discuss possible applications of this game-theoretic model to real-world interactions, such as litigation, tax evasion, and domestic or international diplomacy. They also suggest modifications of the game either for use in class or as student exercises. For reference, they conclude with a brief history of game-theoretic treatments of poker. © 2008 Heldref Publications.
• Shachat, J., & Walker, M. (2004). Unobserved heterogeneity and equilibrium: An experimental study of Bayesian and adaptive learning in normal form games. Journal of Economic Theory, 114(2), 280-309.
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  Abstract: We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects' learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model. © 2003 Published by Elsevier Science (USA).
• Rosenthal, R. W., Shachat, J., & Walker, M. (2003). Hide and seek in Arizona. International Journal of Game Theory, 32(2), 273-293.
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  Abstract: Laboratory subjects repeatedly played one of two variations of a simple two-person zero-sum game of "hide and seek". Three puzzling departures from the prescriptions of equilibrium theory are found in the data: an asymmetry related to the player's role in the game; an asymmetry across the game variations; and positive serial correlation in subjects' play. Possible explanations for these departures are considered.
• Cox, J. C., Shachat, J., & Walker, M. (2001). An Experiment to Evaluate Bayesian Learning of Nash Equilibrium Play. Games and Economic Behavior, 34(1), 11-33.
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  Abstract: We report on an experiment designed to evaluate the empirical implications of Jordan's model of Bayesian learning in games of incomplete information. A finite example is constructed in which the model generates unique predictions of subjects' choices in nearly all periods. When the "true" game defined by players' private information was one with a unique equilibrium in pure strategies, the experimental subjects' play converged to the equilibrium, as Jordan's theory predicts, even when the subjects had not attained complete information about one another. But when there were two pure strategy equilibria, the theory's predictions were not consistent with observed behavior. Journal of Economic Literature Classification numbers: D83, C72, C92. © 2001 Academic Press.
• Walker, M., & Wooders, J. (2001). Minimax play at Wimbledon. American Economic Review, 91(5), 1521-1538.
• Cox, J. C., & Walker, M. (1998). Learning to play Cournot duopoly strategies. Journal of Economic Behavior and Organization, 36(2), 141-161.
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  Abstract: The paper reports results from experiments designed to determine whether subjects can learn to play Cournot duopoly strategies and whether their out-of-equilibrium play is consistent with the predictions of learning models. The experiments include duopolies with constant and with decreasing marginal costs, and with theoretically stable and unstable equilibria. After a few periods, subjects do play stable interior equilibria but they do not play stable boundary equilibria nor unstable interior equilibria. Subjects' out-of-equilibrium play is inconsistent with the predictions of the learning models.
• Moreno, D., & Walker, M. (1994). Two Problems in Applying Ljung′s "Projection Algorithms" to the Analysis of Decentralized Learning. Journal of Economic Theory, 62(2), 420-427.
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  Abstract: We show that Ljung′s projection algorithms, which have recently been used by economists to establish convergence to rational expectations equilibrium, do not seem to apply to learning or forecasting behavior that one would normally call "decentralized." If the algorithm is defined in a way that allows individuals to have differing information, then Ljung′s theorem does not apply. And even if a similar theorem could be proved that would allow for differing information, there remains a Lyapunov-like condition that is central to Ljung′s projection method and which requires that individual beliefs be narrowly related to the equilibrium and to one another. Journal of Economic Literature Classification Numbers: D83, D84, C72, D82. © 1994 Academic Press. All rights reserved.
• Moreno, D., & Walker, M. (1991). Nonmanipulable voting schemes when participants' interests are partially decomposable. Social Choice and Welfare, 8(3), 221-233.
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  Abstract: Recent papers by Barberá and Peleg and by Zhou have established that the Gibbard-Satterthwaite Theorem remains valid when individuals are restricted to reporting only "reasonable" preferences. We present a theorem that covers situations in which, as in Barberá-and-Peleg and Zhou, preferences may be restricted to reasonable ones, but in which, additionally, it may be known in advance that some dimensions of the social decision do not affect all the participants - i.e., in which the social decisions are partially decomposable into decisions that affect only subsets of the participants. As in the previous theorems, the conclusion of this new theorem is that nonmanipulable voting schemes must be dictatorial. © 1991 Spring-Verlag.
• Campbell, D. E., & Walker, M. (1990). Maximal elements of weakly continuous relations. Journal of Economic Theory, 50(2), 459-464.
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  Abstract: A weaker than usual continuity property is defined for binary relations. Relations that have this property, along with certain transitivity properties, are shown to have maximal elements on compact sets. The results cover "interval orders," the kind of relations that often characterize choice situations in which similar alternatives are indistinguishable. © 1990.
• Walker, M., & Hurwicz, L. (1990). On the Generic Non-optimality of Dominant-Strategy Allocation Mechanisms. Econometrica, 58, 683-704.
• Walker, M. (1989). Conflicting interests, decomposability, and comparative statics. Mathematical Social Sciences, 18(1), 57-79.
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  Abstract: When optimizing an aggregate of several individual objective functions, it may be possible to decompose the set of individual objectives into groups across which there are no conflicting interests. It is shown that changes in an individual objective will affect those individuals, and only those individuals, whose objective is in potential conflict with the changed objective. Thus, in particular, each individual can affect every other individual if and only if the optimization problem is indecomposable - i.e. if and only if it is impossible to separate the individuals into groups across which there are no conflicting interests. © 1989.
• Kim, O., & Walker, M. (1984). The free rider problem: Experimental evidence. Public Choice, 43(1), 3-24.
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  Abstract: We have described a number of 'invalidating factors,' any one of which, if present, could account for the weakness or absence of the free rider problem in the voluntary provision of a public good. When any of these factors is present, the free rider phenomenon is not necessarily an implication of economic theory. These invalidatingg factors have been used as a guide in the construction of an experiment which, by avoiding all such factors, should exhibit the free rider phenomenon. The results of performing the experiment indicate that the free rider hypothesis should not be rejected. The contrast between this result and previous experimental results indicates that some of the factors we have identified will be important in attempting to explain the presence or absence of the free rider phenomenon in any particular situation in which a public good is to be financed by voluntary means. © 1984 Martinus Nijhoff Publishers.
• Walker, M. (1984). A simple auctioneerless mechanism with Walrasian properties. Journal of Economic Theory, 32(1), 111-127.
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  Abstract: A simple mechanism for reallocating holdings is described, in which no auctioneer is required: outcomes are determined solely from traders' actions and without any requirement that the mechanism be in equilibrium. The mechanism is shown to exactly duplicate the performance of the Walrasian auctioneer (both in its equilibria and in its disequilibrium path) if individuals are price takers, and, if the number of individuals is large, to approximately duplicate the auctioneer's performance even when individuals behave strategically, each taking account of his own influence on prices. © 1984.
• Walker, M., & Muench, T. (1983). Are Groves-Ledyard Equilibria Attainable?. Review of Economic Studies, 50(2), 393-396.
• Walker, M. (1981). A Simple Incentive-Compatible Scheme for Attaining Lindahl Allocations. Econometrica, 49(1), 65-71.
• Walker, M. (1980). On the nonexistence of a dominant strategy mechanism for making optimal public decisions.. Econometrica, 48(6), 1521-1540.
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  Abstract: In a broad class of situations not covered by the Gibbard-Satterthwaite Theorem it is shown that one cannot design a strategy-proof choice mechanism which attains Pareto optimal outcomes. The results are shown to be generic in character - ie. any non-manipulable mechanism will attain nonoptimal outcomes virtually everywhere - and they cover, in particular, certain problems of allocating public and private goods. The analysis carried out in transferable utility environments, and makes extensive use of the mechanisms recently introduced by Groves.- Author
• Walker, M. A. (1979). A Generalization of the Maximum Theorem. International Economic Review, 20(1), 267-272.
• Walker, M. (1978). On the Characterization of Mechanisms for the Revelation of Preferences. Econometrica, 46(1), 147-152.
• Walker, M. (1977). On the existence of maximal elements. Journal of Economic Theory, 16(2), 470-474.
• Walker, M. (1977). On the informational size of message spaces. Journal of Economic Theory, 15(2), 366-375.
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  Abstract: In a recent paper, Mount and Reiter established that, in a certain sense, the competitive mechanism is an "informationally most efficient" procedure for allocating resources. This result, of course, depends upon the way in which we characterize the notion of informational efficiency. Several alternative characterizations, and the relationships among them, are given here, and it is shown under which characterizations the above result is true, and under which it is false. It is shown that there is an intuitively appealing "best" characterization for which it is true. © 1977.