Martin J. Osborne, "Strategic and extensive games"
[abstractThe basic theory of strategic and extensive games is described. Strategic games, Bayesian games, extensive games with perfect information, and extensive games with imperfect information are defined and explained. Among the solution concepts discussed are Nash equilibrium, correlated equilibrium, rationalizability, subgame perfect equilibrium, and weak sequential equilibrium.],
New Palgrave Dictionary of Economics, 2nd Edition (Steven Durlauf and Lawrence Blume, eds.), volume 8, 21–32. Basingstoke: Palgrave
Martin J. Osborne and Rabee Tourky, "Party formation in single-issue politics"
[abstractWe study the implications of economies of party size in a model of party formation. We show that when the policy space is one-dimensional, candidates form at most two parties. This result does not depend on the magnitude of the economies of party size or sensitively on the nature of the individuals' preferences. It does depend on our assumptions that the policy space is one- dimensional and that uncertainty is absent; we study how modifications of these assumptions affect our conclusions],
Journal of the European Economic Association, 6 (2008), 974–1005.
Martin J. Osborne, Jeffrey S. Rosenthal, and Matthew A. Turner, "Meetings with costly participation: reply"
[abstractThis note corrects an error in an example in "Meetings with Costly Participation" (AER 90(4), 927-943). It characterizes the set of equilibria for the example under the assumptions in the paper, shows that in all the equilibria an interval of moderate positions is devoid of participants, and provides assumptions under which the result as originally stated is correct.],
American Economic Review, 95 (2005),
Martin J. Osborne and Ariel Rubinstein, "Sampling equilibrium, with an application to strategic voting"
[abstractWe suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.],
Games and Economic Behavior45 (2003),
Martin J. Osborne, "Entry-deterring policy differentiation by electoral candidates"
[abstractThis paper studies the equilibria of a one-dimensional spatial model in which three candidates seek to maximize their probabilities of winning, are uncertain about the voters’ preferences, and may move whenever they wish. In the presence of enough uncertainty there is an equilibrium in which two candidates enter simultaneously at distinct positions in the first period and either the third candidate does not enter or enters between the first two in the second period.],
Mathematical Social Sciences40 (2000), 41–62.
Martin J. Osborne, Jeffrey S. Rosenthal, and Matthew A. Turner, "Meetings with costly participation"
[abstractWe study a collective decision-making process in which people interested in an issue may participate, at a cost, in a meeting, and the resulting decision is a compromise among the participants' preferences. We show that the equilibrium number of participants is small and their positions are extreme, and when the compromise is the median, the outcome is likely to be random. The model and its equilibria are consistent with evidence on the procedures and outcomes of U.S. regulatory hearings.],
American Economic Review90 (2000), 927–943.
Martin J. Osborne and Ariel Rubinstein, "Games with procedurally rational players"
[abstractWe study interactive situations in which players are boundedly rational. Each
player, rather than optimizing given a belief about the other players' behavior, as in the theory of Nash equilibrium, uses the following choice procedure. She first associates one consequence with each of her actions by sampling (literally or virtually) each of her actions once. Then she chooses the action that has the best consequence. We define a notion of equilibrium for such situations and study its properties.],
American Economic Review88 (1998), 834–847.
Martin J. Osborne and Al Slivinski, "A model of political competition with citizen-candidates"
[abstractWe develop a model of electoral competition in which citizens choose whether or not to run as candidates. A winner implements her favorite policy. The equilibrium number of candidates depends negatively on the cost of running and positively on the benefits of winning. For some parameter values all equilibria under plurality rule have exactly two candidates, whose positions are distinct. Two-candidate elections are more likely under plurality rule than under a runoff system (cf. Duverger's Law). The candidates' positions are less differentiated under a runoff system. There exist equilibria under both systems in which some candidates have no chance of winning.],
Quarterly Journal of Economics111 (1996), 65–96.
Martin J. Osborne, "Spatial models of political competition under plurality rule: a survey of some explanations of the number of candidates and the positions they take"
[abstractThis paper surveys work that uses spatial models of political competition to explain the number of candidates and the positions that they take in plurality rule elections.],
Canadian Journal of Economics27 (1995), 261–301.
Jean-Pierre Benoît and Martin J. Osborne, "Crime, punishment, and social expenditure"
[abstractCriminal activity can be controlled by punishment, and by social expenditure on both enforcement and redistributive transfers that increase the opportunity cost of imprisonment. Individuals may differ in the combinations of these policies that they prefer. We study the dependence of these preferences on the individuals' characteristics and the nature of the crime under consideration. A political mechanism determines the policy adopted by society. Differences in the policies adopted across societies are explained by the nature of the political mechanism and the initial distribution and level of incomes],
Journal of Institutional and Theoretical Economics151 (1995), 326–347.
Martin J. Osborne, "Candidate positioning and entry in a political competition"
[abstractI first show that if there are more than two potential candidates in the Hotelling–
Downs model of the simultaneous choice of positions by politicians then an equilibrium fails to exist in a wide range of situations. Subsequently I study a temporal model in which candidates are free to act whenever they wish. For the case of three potential candidates I find that in every equilibrium exactly one candidate enters. There is always an equilibrium in which the position chosen by the entrant is the median; the only other possibility is that the position chosen is far from the median.],
Games and Economic Behavior5 (1993), 133–151.
Martin J. Osborne, "Signaling, forward induction, and stability in finitely repeated games"
[abstractIn a finitely repeated two-person game, suppose that after a deviation by player i from the path P in period t there is only one continuation path Q in which player i's payoff from period t on is higher than it is in P. Suppose also that player j cannot benefit from deviating from Q, whatever outcomes ensue. Then it is shown that the path P is not stable in the sense of Kohlberg and Mertens (Econometrica 54 (1986), 1003–1037). It follows that, in a repeated game of coordination, among the set of pure outcome paths which consist of sequences of one-shot Nash equilibria, only those with payoffs very nearly Pareto efficient are stable.], Journal of Economic Theory50 (1990), 22–36.
Martin J. Osborne and Carolyn Pitchik, "Equilibrium in Hotelling's model of spatial competition"
[abstractWe study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames
possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect.
A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations.
Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional "sales" by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.],
[supplementary material: details of derivation of equation (1),
details of arguments in Appendix 1, notes on points (a) and (i) of Appendix 1, calculations referred to at top of page 921, February 1985 version of paper], Econometrica55
Martin J. Osborne and Carolyn Pitchik, "Cartels, profits, and excess capacity" [Working paper version, March 1983]
[abstractWe study a model of a collusive duopoly in which each firm has limited capacity. The negotiated output quotas depend on the bargaining power of the firms, which derives from the damage they can do by cutting prices. If the
capacities are fixed, then th.e unit profit of the small firm is at least as large as that of the large firm, and the relative position of the small firm is better when demand is low. If the capacities can be chosen once-and-for-all, then in equilibrium there is excess capacity so long as the cost of capacity is not too high. This is because a larger capacity permits more damaging threats, so that an extra unit of capacity may be valuable even if it is not used in production.],
International Economic Review 28 (1987), 413–428.
Martin J. Osborne and Carolyn Pitchik, "The nature of equilibrium in a location model" [Working paper version, April 1985]
[abstractThis paper studies the Nash equilibria of Hotelling's pure location model (in which the space of location is a line segment and there is no price variable). It is shown that there is always a symmetric equilibrium in mixed strategies with certain properties, and that as the number of firms increases, the limiting equilibrium mixed strategy of each firm is equal to the distribution function of consumers on the line segment. For the case in which there are three firms and the distribution of consumers is uniform, a detailed analysis of the asymmetric equilibria is given.],
International Economic Review 27 (1986), 223–237.
Martin J. Osborne and Carolyn Pitchik, "Price competition in a capacity-constrained duopoly"
[Working paper version, March 1983]
[abstractThis paper characterizes the set of Nash equilibria in a model of price-setting duopoly in which each firm has limited capacity, and demand is continuous and decreasing. In general there is a unique equilibrium, so that comparative static exercises are meaningful. The properties of the equilibrium conform with a number of stylized facts. The equilibrium prices are lower, the smaller is demand relative to capacity. When demand is in an intermediate range, the firms use mixed strategies-they randomly hold "sales." If capacities are chosen simultaneously, before prices, the set of equilibrium capacities coincides with the set of Cournot quantities.],
Journal of Economic Theory 38 (1986), 238–260.
Martin J. Osborne, "The role of risk aversion in a simple bargaining model"
[abstractThe purpose of this paper is to study the effect of a change in an individual's degree of risk aversion on the perfect Bayesian Nash equilibrium in a simple model of bargaining. I find that, contrary to the results in the axiomatic model with riskless outcomes due to Nash, an opponent may be made worse off by such a change. Further, an individual may want to
take an action that identifies him as more, rather than less, risk averse than he really is. In the course of the analysis, I fully characterize the equilibria of a class of "wars of attrition" with incomplete information, and single out one as "perfect" in a certain sense; this result may be of independent interest.],
pp. 181–213 in Alvin E. Roth (ed.), Game-Theoretic Models of Bargaining, Cambridge University Press, 1985.
Martin J. Osborne, "Why do some goods bear higher taxes than others?"
[abstractTaxation in an economy containing land and labor is studied. The tax system is a compromise based on the relative power of all groups of individuals. (The model extends one of Aumann and Kurz.) In response to the threat of taxation by a majority, individuals can evade taxation of their labor-time (by destroying it), but cannot avoid taxation of the land they own. One result is that the compromise tax rate on land is higher than that on labor. This contrasts with the classical normative result that in order to minimize the efficiency loss, this tax rate should be higher.],
Journal of Economic Theory 32 (1984), 301–316.
Martin J. Osborne, "Capitalist-worker conflict and involuntary unemployment"
[abstractWe study a simple model of the determination of the level of employment in which a capitalist decides how many workers to hire, and then bargains over the wage with those whom he hires. If the capitalist hires all the available workers, his position is weak since, in the event of a strike, he is unable to hire strike-breakers; for this reason he chooses to leave some workers ("involuntarily") unemployed. An increase in unemployment benefits which raises the cost of hiring strike-breakers affects the bargaining power of both capitalist and workers; under some conditions it leads to a reduction in unemployment.],
Review of Economic Studies 51 (1984), 111–127.
Martin J. Osborne and Carolyn Pitchik, "Profit-sharing in a collusive industry"
[abstractWe study a model in which collusive duopolists divide up the monopoly profit according to
their relative bargaining power. We are particularly interested in how the negotiated profit shares depend on the sizes of the firms. If each can produce at the same constant unit cost up to its capacity, we show that the profit per unit of capacity of the small firm is higher than that of the large one. We also study how the ratio of the negotiated profits depends on the size of demand relative to industry capacity, and how this ratio changes with variations in demand.],
European Economic Review 22 (1983), 59–74.
Sean Horan, Martin J. Osborne, and M. Remzi Sanver, "Positively responsive collective choice rules and majority rule: a generalization of May's theorem to many alternatives" [paper]
[abstractA collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative x is in the set selected by a collective choice rule for some collective choice problem. Now suppose that x rises above another selected alternative y in some individual's preferences. If the collective choice rule is "positively responsive", x remains selected but y is no longer selected. If the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule (May 1952).
If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of "independence of irrelevant alternatives" for the domain of problems that have strict Condorcet winners. Further, no rule satisfies the four conditions for the domain of all preference relations.],
July 2017, revised March 2018
Martin J. Osborne, Jeffrey S. Rosenthal, and Colin Stewart, "Information aggregation with costly reporting" [paper]
[abstractA group of individuals with common interests has to choose a binary option
whose desirability depends on an unknown binary state of the world.
The individuals independently and privately observe a signal of the state.
Each individual chooses whether to reveal her signal, at a cost. We show
that if for all revelation choices of the individuals the option chosen by the
group is optimal given the signals revealed and the set of individuals who
do not reveal signals, then in a large group few signals are revealed, and
these signals are extreme. The correct decision is taken with high probability
in one state but with probability bounded away from one in the other.
No anonymous decision-making mechanism without transfers does better.
However, the first-best average payoff can be attained using transfers
among agents, and approximately attained with a non-anonymous mechanism
September 2016, revised June 2017.
Martin J. Osborne, "Darwin, Fisher, and a theory of the evolution of the sex ratio" [paper]
[abstractA theory of the evolution of the sex ratio, universally attributed to Fisher (The genetical theory of natural selection, 1930) is contained in the first edition of Darwin’s Descent of man (1871). I raise the question of why Darwin eliminated the theory from the second edition.],
May 1996, revised July 1996.