Mark W Stegeman

Interests

No activities entered.

Courses

Scholarly Contributions

Journals/Publications

• Komai, M., & Stegeman, M. (2010). Leadership based on asymmetric information. RAND Journal of Economics, 41(1), 35-63.
  More info

  Abstract: Rational players, unconstrained by contracts or formal authority, choose to follow a better-informed leader, whose action reveals part of her information. If the leader satisfies a credibility condition, then the unique nondegenerate equilibrium solves distinct shirking and coordination problems and achieves the first best. If credibility fails, as is more likely for a large organization, then followers ignore the leader, and equilibria are very inefficient. Appointing multiple leaders, or a high-cost leader, can restore credibility. If players invest privately in information, then a leader often appears endogenously. The equilibrium concept is an original extension of sequential equilibrium to continuous states. © 2010, RAND.
• Komai, M., Stegeman, M., & Hermalin, B. E. (2007). Leadership and information. American Economic Review, 97(3), 944-947.
• Stegeman, M., & Rhode, P. (2004). Stochastic Darwinian equilibria in small and large populations. Games and Economic Behavior, 49(1), 171-214.
  More info

  Abstract: We establish necessary and sufficient conditions for the stability of stochastic Darwinian dynamics in quadratic games. Each player's strategy adjusts through mutation and selection shocks, and stability is independent of the rates at which these shocks arrive. Given stability, we characterize the midpoint of the nondegenerate ergodic distribution. In small populations, some equilibria correspond to relative payoff maximization, but others are unanticipated by existing static concepts. In the large population limit of a finite population, the set of stable Nash equilibria strictly includes all equilibria stable under myopic best reply, but some strict Nash equilibria are highly unstable. The stability result shows, for the first time, that large finite populations converge to Nash play even if they do not understand the game and strategies are so numerous that most are never played. The large population stability condition is related to risk dominance and, separately, to the static CSS condition. © 2003 Elsevier Inc. All rights reserved.
• Dufwenberg, M., & Stegeman, M. (2002). Existence and uniqueness of maximal reductions under iterated strict dominance. Econometrica, 70(5), 2007-2023.
  More info

  Abstract: Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well-defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better-reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.
• Gale, I. L., & Stegeman, M. (2001). Sequential auctions of endogenously valued objects. Games and Economic Behavior, 36(1), 74-103.
  More info

  Abstract: Two completely informed but possibly asymmetric bidders buy or sell identical "claims" in sequential auctions. They subsequently receive monetary prizes that depend upon the final allocation of claims. Iterated elimination of weakly dominated strategies leaves a unique Nash equilibrium. For any prize schedule, prices weakly decline as the auctions progress, and points of strict decline have a simple characterization. For one class of prize schedules, which arises naturally if duopolists bid for a scarce input, the equilibrium is completely characterized; many initial allocations generate the same final (unequal) division of claims, which may be interpreted as the natural market structure. Journal of Economic Literature Classification Numbers: D43, D44, L11. © 2001 Academic Press.
• Rhode, P., & Stegeman, M. (2001). Non-Nash equilibria of Darwinian dynamics with applications to duopoly. International Journal of Industrial Organization, 19(3-4), 415-453.
  More info

  Abstract: Consider a symmetric, differentiated duopoly. If firms' strategy choices, in the repeated game, follow a stochastic Darwinian process, then they cluster around a strategy profile that is typically not a one-shot Nash equilibrium. This profile is invariant under a broad class of transformations of the strategy space (e.g. Bertrand vs. Cournot); this implies that mixing imitative and rational decision-makers can produce purely imitative outcomes. The evolution of objectives consistently distorts behavior toward revenue maximization, and the distortion increases in 'good times' of high demand and low costs. We generalize the results beyond duopoly to symmetric, two-player games. © Elsevier Science B.V.
• Gale, I. L., Hausch, D. B., & Stegeman, M. (2000). Sequential procurement with subcontracting. International Economic Review, 41(4), 989-1020.
  More info

  Abstract: Two symmetric sellers are approached sequentially by fragmented buyers. Each buyer conducts a second-price auction and purchases from the seller who offers the lower price. Winning an auction affects bidding for future contracts because the sellers have nonconstant marginal costs. We assume that the sellers are completely informed, and we study the unique equilibrium that survives iterated elimination of weakly dominated strategies. If subcontracting between the sellers is impossible, the final allocation of contracts is generally inefficient. If postauction subcontracting is possible, the sellers can be worse off, ex ante, than when subcontracting is impossible.
• Gale, I., Hausch, D. B., & Stegeman, M. W. (2000).

  Sequential Procurement Auctions with Subcontracting

  . International Economic Review, 41, 989-1021.
• Stegeman, M. (2000). Rigid monopoly prices. Advances in Applied Microeconomics, 9, 231-263.
  More info

  Abstract: A consumer in the real world typically must visit (e.g. by phone) a monopolist to observe its price, even though the consumer may have correct expectations about that price. This causes monopoly prices to be higher and stickier than is predicted by the textbook model. If visiting costs are small, and consumers do not observe the firm's costs, then prices conform to the textbook model when costs are high but are downwardly rigid when costs drop below a threshold. Price flexibility increases as the fraction of ignorant consumers, who observe their idiosyncratic valuations of the product only after visiting the firm, increases. In a repeated game, a 'ratchet' equilibrium, in which price increases are permanent and price decreases temporary within a certain band, supports equilibria for which price is rigid on the equilibrium path but which Pareto dominate the fluctuating one-shot equilibrium. The ratchet equilibrium has the advantages that price is a continuous function of past prices near the equilibrium path and the price coordination problem is solved in a natural way: the equilibrium price is the lowest price that can be sustained by such a ratchet. This equilibrium price exceeds but is close to the average prediction of the textbook model. Additional results are derived for the case in which costs are fixed. © 2000.
• Rhode, P. W., & Stegeman, M. (1996).

  A COMMENT ON "LEARNING, MUTATION, AND LONG-RUN EQUILIBRIA IN GAMES"

  . Econometrica, 64(2), 443-449. doi:10.2307/2171792
  More info

  mutation.) Kandori, Mailath, and Rob (henceforth KMR) first provide a useful general theorem concerning the stationary distribution of strategies under Darwinian dynamics. They then divide the analysis of the 2 x 2 game into three cases: dominant strategy games (e.g., prisoners' dilemma), coordination games, and games with no symmetric pure strategy equilibrium (e.g., battle of the sexes). We refer to these as DS, C, and NP games. In each case, KMR claim that, as the rate of mutation vanishes, the stationary distribution of strategies converges to a symmetric Nash equilibrium. They emphasize C games, which have two symmetric Nash equilibria, and characterize the conditions under which the distribution converges to the risk dominant equilibrium. In this note, we argue that while their formal conclusions for C games are correct, their results for DS and NP games are valid only for large populations of players. In small populations, Darwinian dynamics may produce non-Nash outcomes in these two cases. Section 1 summarizes the KMR model, and Section 2 provides examples of 2 x 2 games in which Darwinian dynamics generate non-Nash outcomes. A theorem in Section 3 describes the Darwinian equilibrium of any 2 x 2 game.
• Rhode, P., & Stegeman, M. (1996). A comment on: 'Learning, mutation, and long-run equilibria in games'. Econometrica, 64(2), 443-449.
  More info

  Abstract: In a recent article in this journal, Kandori, Mailath, and Rob (1993) (KMR) study the Darwinian dynamics of a 2x2 symmetric game, played repeatedly within a finite population. KMR first provide a useful general theorem concerning the stationary distribution of strategies under Darwinian dynamics. They then divide the analysis of the 2x2 game into three cases : dominant strategy (DS) games (e.g., prisoners' dilemma), coordination (C) games, and games with no symmetric pure strategy equilibrium ( NP) (e.g., battle of the sexes). In each case, KMR claim that, as the rate of mutation vanishes, the stationary distribution of strategies converges to a symmetric Nash equilibrium. They emphasize C games, which have two symmetric Nash equilibria, and characterize the conditions under which the distribution converges to the risk dominant equilibrium. In this note, we argue that while their formal conclusions for C games are correct, their results for DS and NP games are valid only for large populations of players. In small populations, Darwinian dynamics may produce non-Nash outcomes in these two cases.
• Stegeman, M. (1996). Participation costs and efficient auctions. Journal of Economic Theory, 71(1), 228-259.
  More info

  Abstract: Suppose that risk neutral agents have independently (and perhaps asymmetrically) distributed private valuations for an indivisible object. A mechanism assigns the object, but it is costly to send messages to the coordinator. In these circumstances, the second-price auction has an equilibrium that is classically ex ante efficient, given general opportunities to invest in information about or enhancements of own valuations. In contrast, the first-price sealed bid auction may have no efficient equilibrium, even if buyers are symmetric. Other properties of the first-price auction are proved. A semirevelation principle is established for mechanisms with participation costs. Journal of Economic Literature Classification Numbers: D44, D82. © 1996 Academic Press, Inc.
• Gale, I., & Stegeman, M. W. (1994).

  Exclusion in all-pay auctions

  . Working Paper.
  More info

  A description of a procedure for increasing the seller's expected revenue in an all-pay auction, specifically in the case of lobbying, where a politician is typically assumed to award the political prize to the highest bidder.
• Stegeman, M. (1993).

  SUFFICIENT CONDITIONS FOR INESSENTIALITY

  . Econometrica, 61(3), 613-628. doi:10.2307/2951720
  More info

  Three theorems state conditions sufficient for the inessentiality of equilibrium in a pure exchange, sequence economy. The agents have uncommon priors, state-contingent utility functions, and asymmetric information in every trading period, and they trade different sets of event-contingent claims in different periods. The theorems provide alternative interpretations of the concept of market completeness, reveal two fundamentally different ways to obtain inessentiality, and shed light on the conditions permitting speculation and the role of price-contingent trading. None of the theorems requires ex ante Pareto optimality or the absence of arbitrage opportunities. Copyright 1993 by The Econometric Society.

Presentations

• Stegeman, M. W., & Rhode, P. (2015, April). Voting With Process Payoffs and Partial Enactment. UA Internal seminar.