Much of Mark's research in recent years has been supported by the National Science Foundation. The NSF's support has been instrumental in each of the papers listed below, and several data sets have been generated from this research. These data sets are available for other researchers to use.
In addition to the research papers listed below, two recent expository papers on mixed-strategy equilibrium are available as well:
Recent Research Papers
Games and Economic Behavior, forthcoming.
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.
Games and Economic Behavior, Vol. 71 (2011), 487-502.
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, and in which the winner of the match is determined by the winning of points, in "point games." We call such 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 (thus, playing minimax at each point assures a player that the probability he will win the match is at least as great as under equilibrium play, no matter how his opponent plays); 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. The minimax result provides a rationale for the players to play minimax (and therefore Nash equilibrium) in every point game, even if the behavioral assumptions typically used to justify Nash equilibrium are not satisfied. An application to tennis is provided.
Review of Economic Design, Vol. 13 (2009), 101-114.
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.
Journal of Experimental Economics, forthcoming.
When second-price auctions have been conducted in the laboratory, most of the observed bids have been "overbids" (bids that exceed the bidder's value) and there are very few underbids. Few if any of the subjects in those experiments had any prior experience bidding in auctions. 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 tend not to bid their values, suggesting that the non-optimal bidding of novice subjects is robust to substantial experience in non-experimental auctions. A key determinant of bidding behavior was whether a subject had ever been a seller on eBay.
Journal of Economic Theory, Vol. 114 (2004), 280-309.
A demo of the experiment is available as well.
We describe an experiment based on a repeated two-person game of incomplete information designed so that Jordan's Bayesian model of learning in games and the best response model make completely opposite predictions. Econometric analysis of the experimental data, using the maximum likelihood procedure due to El Gamal and Grether, reveals clear heterogeneity in the subjects' learning behavior. The heterogeneity is not diffuse, however: the subjects follow only a few decision rules for basing their play on their information, and their decision rules have simple cognitive interpretations. Although the repeated game has many equilibria, including a unique pure strategy equilbrium, 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, in a "representative player" sense, each subject using a pure strategy, but the distribution of strategies among subjects coinciding with the mixed strategy equilbrium.
International Journal of Game Theory, Vol. 32 (2003), 273-293.
Laboratory subjects repeatedly played one of two variations of a simple two-person zero-sum game of pursuit and evasion. 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.
American Economic Review, Vol. 91 (2001), 1521-1539.
We use data from classic professional tennis matches to provide an empirical test of the minimax hypothesis. We find that the serve-and-return play of John McEnroe, Bjorn Borg, Boris Becker, Pete Sampras and others is largely consistent with the minimax hypothesis. The same statistical tests soundly reject the assumption of minimax play in experimental data, including the data from Barry O'Neill's celebrated experiment. [A more extended abstract for the non-technical reader is available as well.]
Games and Economic Behavior, Vol. 34, (2001), 11-33;
Some recent theoretical approaches to the question of how players might converge over time to a Nash equilibrium have assumed that the players update their beliefs about other players via Bayes' Rule. Jordan has shown in a Bayesian model of this kind that play will (theoretically) always converge to a complete-information Nash equilibrium, even though individual players will not generally attain complete information. We report on an experiment designed to evaluate the empirical implications of Jordan's model. A finite version of the model is constructed which generates unique predictions of subjects' choices in nearly all periods. The experimental data reveals that the theory does reasonably well at predicting the equilbria that subjects eventually play, even when there are multiple equilibria. The results thus suggest that Jordan's Bayesian model can provide an empirically effective solution to the equilibrium selection problem when the players have beliefs with finite support. However, the model's predictions about the path of play over time are not consisitent with the experimental data.
Journal of Economic Behavior and Organization, Vol. 36 (1998), 141-161.
In most theories of out-of-equilibrium play or "learning" in games, the stability of Cournot equilibrium depends upon how the firms' reaction functions cross. In particular, if the firms' marginal costs decline rapidly enough with increased output, then the interior equilibrium will be (theoretically) unstable. We report on a series of experiments designed to determine whether interior Cournot equilibria are attained in such theoretically unstable environments. The experiments include duopolies with constant and with decreasing marginal costs, and with theoretically stable and unstable equilibria. The experimental results reveal a sharp distinction between behavior in the stable and the unstable duopolies: after a few early periods, play in the stable duopolies is at or near the equilibrium, and in the unstable duopolies it is almost never at or near the interior equilibrium.
Journal of Economic Theory, Vol. 62 (1994), 420-427.
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.
Social Choice & Welfare, Vol. 8 (1991), 221-233.
Recent papers by Barbera 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 Barbera & 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.
Econometrica, Vol. 58 (1990), 683-704.
It is shown that if an economy's participants cannot be separated into groups across which there are no potentially conflicting interests -- i.e., if the economy is "indecomposable" -- then every continuous truth-dominant allocation mechanism will attain nonoptimal allocations on an open dense set of preference profiles. Classical "Edgeworth-box" exchange economies (economies with no externalities and no production, but with arbitrary numbers of consumers and goods), as well as economies with public goods and economies with other kinds of externalities, are all shown via simple arguments to be indecomposable. The results are extended to cover nonrevelation mechanisms that have dominant-strategy equilibria.
Journal of Economic Theory, Vol. 50 (1990), 459-464.
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.
Mathematical Social Sciences, Vol. 18 (1989), 57-79.
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.
Journal of Economic Theory, Vol. 32 (l984), 111-127.
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.
Public Choice, Vol.43 (l984), 3-24.
Review of Economic Studies, Vol. 50 (l983), 393-396.
Econometrica, Vol. 49 (l98l), 65-7l.
A simple scheme is presented for making decisions about the production and financing of public goods. The "competitive" equilibria under the scheme are Pareto optimal; more important, they are Lindahl equilibria. Thus, it is never in any individual's interest to refuse to participate (no one will be worse off at the equilibrium than at his initial holding); moreover, the existence of equilibria is assured in the usual classical public-goods economies.
Econometrica, Vol. 48 (l980), l52l-l540.
In a broad class of cases 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 -- i.e., any nonmanipulable mechanism will attain nonoptimal outcomes virtually everywhere -- and the results cover, in particular, certain problems in allocating public and private goods. The analysis is carried out in transferable-utility environments, and makes extensive use of the mechanisms recently introduced by Groves.
International Economic Review, Vol. 19 (l979), 267-272.
Econometrica, Vol. 46 (l978), l47-l52.
Green and Laffont have characterized certain appealing dominant-strategy revelation mechanisms as precisely the mechanisms introduced by Groves, but they have established the characterization only for unstructured sets of public alternatives: if the set has some natural structure, their proof generally requires that pathological preferences be admissible -- for example, discontinuous and/or non-convex preferences. It is shown here that the same characterization holds on sets in Rn, even if we rule out pathological preferences. This greatly extends the usefulness of the characterization.
Journal of Economic Theory, Vol. l6 (l977), 470-474.
Journal of Economic Theory, Vol. l5 (l977), 366-375.
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 depends of course upon the way 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 ones it is false. It is shown that there is an intuitively appealing "best" characterization for which the result is true.