John Wooders joined UTS in June 2011 from the University of Arizona. His personal web page can be accessed by clicking here.
Strategic behavior in games and markets, game theory, mixed-strategy Nash equilibrium, effect of seller reputation on auction prices, incentives of bidders to enter auctions, "mini-micro" foundations of competitive equilibrium
Bochet, O, Nikiforakis, N, Reuben, E, Wooders, J & Wooders, M 2020, 'An introduction to the second special issue commemorating works of James Andreoni, Theodore Bergstrom, Larry Blume, and Hal Varian', Journal of Public Economic Theory, vol. 22, no. 2, pp. 279-284.View/Download from: Publisher's site
Bochet, O, Nikiforakis, N, Reuben, E, Wooders, J & Wooders, M 2019, 'Introduction to the JPET special issues commemorating works of James Andreoni, Theodore Bergstrom, Larry Blume, and Hal Varian', Journal of Public Economic Theory, vol. 21, no. 5, pp. 799-803.View/Download from: Publisher's site
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. We characterize security strategies and payoffs for three mechanisms for dissolving partnerships: the Texas Shoot-Out, the K+ 1 auction, and the compensation auction. A security strategy maximizes a participant’s minimum payoff, and represents a natural starting point for analysis when a participant is either uncertain of the environment or uncertain of whether his rivals will play equilibrium. For the compensation auction, a dynamic dissolution mechanism, we introduce the notion of a perfect security strategy. Such a strategy maximizes a participant’s minimum payoff along every path of play. We show that while a player has many security strategies in the compensation auction, he has a unique perfect security strategy.
© 2016, Springer-Verlag Berlin Heidelberg. When a decision maker is a member of multiple social groups, her actions may cause information to “spill over” from one group to another. We study the nature of these spillovers in an observational learning game where two groups interact via a common player, and where conventions emerge when players follow the decisions of the members of their own groups rather than their own private information. We show that: (i) if a convention develops in one group but not the other group, then the convention spills over via the common player; (ii) when conventions disagree, then the common player’s decision breaks the convention in one group; and (iii) when no convention has developed, then the common player’s decision triggers the same convention in both groups. We also show that information spillovers may reduce welfare, and we investigate the surplus-maximizing timing of spillovers.
We show that risk aversion raises the public reserve price above the seller’s cost , but lowers the secret reserve price below the revenue maximizing reserve price . Further, . Hence, for a risk averse seller, public and secret reserve prices are ordered: .
Minimax and its generalization to mixed strategy Nash equilibrium is the cornerstone of our understanding of strategic situations that require decision makers to be unpredictable. Using a dataset of nearly half a million serves from over 3000 matches, we examine whether the behavior of professional tennis players is consistent with the Minimax Hypothesis. The large number of matches in our dataset requires the development of a novel statistical test, which we show is more powerful than the tests used in prior related studies. We find that win rates conform remarkably closely to the theory for men, but conform somewhat less neatly for women. We show that the behavior in the field of more highly ranked (i.e., better) players conforms more closely to theory.
We study non-stationary dynamic decentralized markets with adverse selection in which trade is bilateral and prices are determined by bargaining. Examples include labor markets, housing markets, and markets for financial assets. We characterize equilibrium, and identify the dynamics of transaction prices, trading patterns, and the average quality in the market. When the horizon is finite, the surplus in the unique equilibrium exceeds the competitive surplus; as traders become perfectly patient the market becomes completely illiquid at all but the first and last dates, but the surplus remains above the competitive surplus. When the horizon is infinite, the surplus realized equals the static competitive surplus. We study policies aimed at improving market performance, and show that subsidies to low quality or to trades at a low price, taxes on high quality, restrictions on trading opportunities, or government purchases may raise the surplus. In contrast, interventions like the Public-Private Investment Program for Legacy Assets reduce the surplus when traders are patient.
© 2016 Elsevier Inc. In financial disputes arising from divorce, inheritance, or the dissolution of a partnership, frequently the need arises to assign ownership of an indivisible item to one member of a group. This paper introduces and analyzes a dynamic auction for simply and efficiently allocating an item when participants are privately informed of their values. In the auction, the price rises continuously. A bidder who drops out of the auction, in return for surrendering his claim to the item, obtains compensation equal to the difference between the price at which he drops and the preceding drop price. When only one bidder remains, that bidder wins the item and pays the compensations of his rivals. We characterize the unique equilibrium with risk-neutral and CARA risk averse bidders. We show that dropout prices are decreasing as bidders become more risk averse. Each bidder's equilibrium payoff is at least 1/N-th of his value for the item.
We explore the role of experience in mixed-strategy games by comparing, for a stylized version of Texas Hold-em, the behavior of experts, who have extensive experience playing poker online, to the behavior of novices. We find significant differences. The initial frequencies with which players bet and call are closer to equilibrium for experts than novices. And, while the betting and calling frequencies of both types of subjects exhibit too much heterogeneity to be consistent with equilibrium play, the frequencies of experts exhibit less heterogeneity. We find evidence that the style of online play transfers from the field to the lab.
Wooders, J 2014, 'Analyzing Wimbledon: The Power of Statistics', Journal of Economic Literature, vol. 52, no. 3, pp. 867-869.
Garratt, R, Walker, M & Wooders, J 2012, 'Behavior in second-price auctions by highly experienced eBay buyers and sellers', Experimental Economics, vol. 15, no. 1, pp. 44-57.View/Download from: Publisher's site
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.
If bidders have independent private values and homogeneous entry costs, a first- or second-price auction with a reserve price equal to the seller's value maximizes social surplus and seller revenue. We show that if entry costs are heterogeneous and private information, then the revenue-maximizing reserve price is above the seller's value, a positive admission fee (and a reserve price equal to the seller's value) generates more revenue, and an entry cap combined with an admission fee generates even more revenue. Social surplus and seller revenue may either increase or decrease in the number of bidders, but they coincide asymptotically.
Shahriar, Q & Wooders, J 2011, 'An experimental study of auctions with a buy price under private and common values', Games and Economic Behavior, vol. 72, no. 2, pp. 558-573.View/Download from: Publisher's site
eBays Buy It Now format allows a seller to list an auction with a buy price at which a bidder may purchase the item immediately and end the auction. When bidders are risk averse, then theoretically a buy price can raise seller revenue when values are private (but not when values are common). We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winners curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model.
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.
Experiments on second-price sealed-bid private value auctions have established that subjects typically bid more than their value, despite the fact that value bidding is a dominant strategy in such auctions. Moreover, the laboratory evidence shows that subjects do not learn to bid their values as they gain more experience. In the present paper, we re-examine the second-price auction data from Kagel and Levin's (Econ J 103:868-879, 1993) classic paper. We find that auction efficiency increases over time, even though the frequency of overbidding is unchanged. We argue that the rise in efficiency is due to a decline in the variability of overbidding. This is consistent with subjects' learning to bid more like each other.
In markets with adverse selection, only low-quality units trade in the competitive equilibrium when the average quality of the good held by sellers is low. We show that under decentralized trade, however, both high-and low-quality units trade, although with delay. Moreover, when frictions are small, the surplus realized is greater than the (static) competitive surplus. Thus, decentralized trade mitigates the lemons problem. Remarkably, payoffs are competitive as frictions vanish, even though both high-and low-quality units continue to trade, and there is trade at several prices.
Does expertise in strategic behavior obtained in the field transfer to the abstract setting of the laboratory? Palacios-Huerta and Volij (2008) argued that the behavior of professional soccer players in mixed-strategy games conforms closely to minimax play, while the behavior of students (who are presumably novices in strategic situations requiring unpredictability) does not. We reexamine their data, showing that the play of professionals is inconsistent with the minimax hypothesis in several respects: (i) professionals follow nonstationary mixtures, with action frequencies that are negatively correlated between the first and the second half of the experiment, (ii) professionals tend to switch between under- and overplaying an action relative to its equilibrium frequency, and (iii) the distribution of action frequencies across professionals is far from the distribution implied by minimax. In each respect, the behavior of students conforms more closely to the minimax hypothesis.
eBay and Yahoo allow sellers to list their auctions with a buy price at which a bidder may purchase the item immediately. On eBay, the buy-now option disappears once a bid is placed, while on Yahoo the buy-now option remains in effect throughout the auction. We show that when bidders are risk averse, both types of auctions raise seller revenue for a wide range of buy prices. The Yahoo format raises more revenue than the eBay format when bidders have either CARA or DARA. Bidders with DARA prefer the eBay auction, while bidders with CARA are indifferent between the two.
Employing a procedure suggested by a simple theoretical model of auctions in which bidders and sellers have observable and heterogenous reputations for default, we examine the effect of reputation on price in a data set drawn from the online auction site eBay. Our main empirical result is that seller's, but not bidder's, reputation has an economically and statistically significant effect on price.
Goeree, J, Plott, C & Wooders, J 2004, 'Bidders' choice auctions: Raising revenues through the right to choose', Journal of the European Economic Association, vol. 2, no. 2-3, pp. 504-515.View/Download from: Publisher's site
Amir, R, Evstigneev, I & Wooders, J 2003, 'Noncooperative versus cooperative R&D with endogenous spillover rates', Games And Economic Behavior, vol. 42, no. 2, pp. 183-207.View/Download from: Publisher's site
This paper deals with a general version of a two-stage model of R&D and product market competition. We provide a thorough generalization of previous results on the comparative performance of noncooperative and cooperative R&D, dispensing in particular with ex-post firm symmetry and linear demand assumptions. We also characterize the structure of profit-maximizing R&D cartels where firms competing in a product market jointly decide R&D expenditure, as well as internal spillover, levels. We establish the firms would essentially always prefer extremal spillovers, and within the context of a standard specification, derive conditions for the optimality of minimal spillover.
We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading pat trier is costly, prices arc determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero. even though the trading patterns continue to be inefficient and delay persists.
We develop a test of the minimax hypothesis using field data from championship professional tennis matches, and we find that win rates in the serve and return play of top professional tennis players are consistent with the minimax hypothesis. However, the players' choices are not consistent with the serial independence implied by the minimax hypothesis: even the best tennis players tend to switch from one action to another too often.
Wooders, J & Moreno, D 2001, 'Prices, Delay, and the Dynamics of Trade', Economics Bulletin, vol. 28, no. 7.
We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading partner is costly, prices are determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero, even though the trading patterns continue to be inefficient and delay persists.
We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the supergame provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Classification Numbers: C72, C9.
Amir, R & Wooders, J 2000, 'One-way spillovers, endogenous innovator/imitator roles, and research joint ventures', Games And Economic Behavior, vol. 31, no. 1, pp. 1-25.View/Download from: Publisher's site
We consider a two-period duopoly characterized by a one-way spillover structure in process R&D and a very broad specification of product market competition. We show that a priori identical firms always engage in different levels of R&D, at equilibrium, thus giving rise to an innovator/imitator configuration and ending up with different sizes. We also provide a general analysis of the social benefits of, and firms' incentive for, forming research joint ventures. Another contribution is methodological, illustrating how submodularity (R&D decisions are strategic substitutes) can be exploited to provide a general analysis of a R&D game. Journal of Economic Literature Classification Numbers: C72, L13, O31.
Amir, R & Wooders, J 1999, 'Effects of one-way spillovers on market shares, industry price, welfare, and R & D cooperation', Journal Of Economics & Management Strategy, vol. 8, no. 2, pp. 223-249.
With one-way spillovers, the standard symmetric two-period R & D model leads to an asymmetric equilibrium only, with endogeneous innovator and imitator roles. We show how R & D decisions and measures of firm heterogeneity-market shares, R & D shares, and profits-depend on spillovers and on R & D costs. While a joint lab always improves on consumer welfare, it yields higher profits, cost reductions, and social welfare only under extra assumptions, beyond those required with multidirectional spillovers. Finally, the novel issue of optimal R & D cartels is addressed. We show an optimal R & D cartel may seek to minimize R & D spillovers between its members.
We consider a model in which firms first choose process R&D expenditures and then compete in an output market. We show the symmetric equilibrium under R&D competition is sometimes unstable, in which case two asymmetric equilibria must also exist. For the latter, we find, in contrast to the literature that total profits are sometimes higher with R&D competition than with research joint venture cartelization (due to the cost asymmetry of the resulting duopoly in the noncooperative case). Furthermore, these equilibria provide another instance of R&D-induced firm heterogeneity.
Moreno Ruiz, D & Wooders, J 1998, 'An experimental study of communication and coordination in noncooperative games', Games And Economic Behavior, vol. 24, no. 1-2, pp. 47-76.View/Download from: Publisher's site
This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate by plain conversation prior to playing a simple game. In this setting, we find that the presumption of individualistic and independent behavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to be coordinated and correlated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof correlated equilibrium of the game, however, explains the data when the possibility of errors by players is introduced.
We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.
We analyze trading in a model in which the agents and their preferences are the same as in the main models of matching and bargaining, but in which trade is centralized rather than decentralized. We characterize equilibrium when trade is centralized and, by comparing our results with results from the matching literature, we show conditions under which decentralized trading processes reproduce the allocations of our centralized one. We establish that the competitive price as defined in the matching literature (i.e.. relative to the stocks. flows, or totals) coincides, in the appropriate setting, with the equilibrium price in our model.
Wooders, J 1997, 'Equilibrium in a Market with Intermediation is Walrasian', The Review of Economic Design 3, vol. 3, no. 1, pp. 75-89.
We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices.
We characterize the agreements that the players of a noncooperative game may reach when they can communicate prior to play, but they cannot reach binding agreements: A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. We show that any correlated strategy whose support is contained in the set of actions that survive the iterated elimination of strictly dominated strategies and weakly Pareto dominates every other correlated strategy whose support is contained in that set, is a coalition-proof equilibrium. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof.
Houser, DE & Wooders, J 2005, 'Hard and soft closes: A field experiment on auction closing rules' in Rapoport, A & Zwick, R (eds), Experimental business research, Vol. 2: Economic and managerial perspectives, Palgrave MacMillan, Germany, pp. 123-131.
Amir, R, Evstigneev, I & Wooders, J 2001, 'Non-cooperative Versus Cooperative R & D with Endogenous Spillover'.
AMIR, R & WOODERS, J 1997, 'One-way spillovers, endogenous innovator/imitator roles and research joint ventures'.
We consider a two-period duopoly characterized by a one-way spillover structure in process R&D and a very broad specification of product market competition. We show that a priori identical firms always engage in different levels of R&D, at equilibrium, thus giving rise to an innovator/imitator configuration and ending up with different sizes. We also provide a general analysis of the social benefits of, and firms’ incentive for, forming research joint ventures. The key properties of the game are submodularity (R&D decisions are strategic substitutes) and lack of global concavity.
Amir, R & Wooders, J, 'Effects of One-way Spillovers on Market Shares, Industry Price, Welfare, and R&D Cooperation'.
With one-way spillovers, the standard symmetric two-period R&D model leads to an asymmetric equilibrium only, with endogenous innovator and imitator. We show how R&D decisions and measures of firm heterogeneity - market shares, R&D shares, and profits - depend on spillovers and on R&D costs. While a joint lab always improves on consumer welfare, it yields higher profits, cost reductions and social welfare only under extra assumptions, beyond those required with multi-directional spillovers. Finally, the novel issue of optimal R&D cartels (with an endogenous spillover parameter) is addressed. In particular, the latter can be zero under some conditions.
Amir, R & Wooders, J, 'One-Way Spillovers, Endogenous Innovator/Imitator Roles andResearch Joint Ventures'.
We consider a two-period duopoly characterized by a one-way
spillover structure in process R&D and a very broad
specification of product market competition. We show that a
priori identical firms always engage in different levels of
R&D, at equilibrium, thus giving rise to an
innovator/imitator configuration and ending up with
different sizes. In view of this endogenous firm
heterogeneity, the social benefits of, and the firms'
incentives for, research joint ventures are somewhat
different from the case of ex post firm symmetry. The key
properties of the game are submodularity (R&D decisions are
strategic substitutes) and lack of global concavity.
Moreno, D & Wooders, J, 'An experimental study of communication and cooperation in noncooperative games.'.
This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate by plain conversation prior to playing a simple game. In this setting, we find that the presumption of individualistic and independent behavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to be cooperative and correlated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof equilibrium of the game, however, explains the data when the possibility of errors by players is introduced.
Moreno, D & Wooders, J, 'An experimental study of communication and coordination in noncooperative games.'.
This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate byplain conversationprior to playing a simple game. In this setting, we find that the presumption ofindividualisticandindependentbehavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to becoordinatedandcorrelated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof correlated equilibrium of the game, however, explains the data when the possibility of errors by players is introduced
Wooders, J & Moreno, D, 'Auctions with heterogeneous entry costs'.
We study the impact of public and secret reserve prices in auctions where buyers have
independent private values and heterogeneous entry costs. We find that in a standard auction the
optimal (i.e., revenue maximizing) public reserve price is typically above the seller's value.
Moreover, an appropriate entry fee together with a public reserve price equal to the seller's
value generates greater revenue. Secret reserve prices, however, differ across auction formats.
In a second-price sealed-bid auction the secret reserve price is above the optimal public reserve
price; hence there is less entry, a smaller probability of sale, and both the seller revenue and
bidders' utility are less than with an optimal public reserve price. In contrast, in a first-price
sealed-bid auction the secret reserve is equal to the seller's value, and the bidders' expected
utility (seller revenue) is greater (less) than with an optimal public reserve price.