Two-party competition with many constituences

The paper considers a single member district, simple plurality political system with n districts. There are two political parties, each consisting of n candidates. Individual candidates seek to win their district per se, but voters appreciate that final policy outcomes will depend upon: (1) which party wins control of the legislature, and (2) how party policy is derived from the party members' policies. Candidates take account of such voter deliberations in choosing their election strategies. A set of minimal sufficient conditions for an equilibrium to exist in this game is provided and the equilibrium characterized. While party policies are shown to converge in equilibrium, candidate policies in general do not - either across or within parties.     

Elections with limited information: A multidimensional model

We develop a game-theoretic model of two-candidate competition over a multidimensional policy space, where the participants have incomplete information about the preferences and strategy choices of other participants. The players consist of the voters and the candidates. Voters are partitioned into two classes, depending on the information they observe. Informed voters observe candidate strategy choices while uninformed voters do not. All players (voters and candidates alike) observe contemporaneous poll data broken-down by various subgroups of the population.The results of the paper give conditions on the number and distribution of the informed and uninformed voters which are sufficient to guarantee that any equilibrium (or voter equilibrium) extracts all information.     

Endogenous platforms: the case of many parties

We analyze existence of equilibrium in a one-dimensional model of endogenous party platforms and more than two parties. The platforms proposed by parties depend on their membership composition. The policy implemented is a function of the different proposals and the vote distribution among such proposals. It is shown that if voters are sincere there is always an equilibrium regardless of the number of parties. In the case of strategic voting behavior, existence of equilibrium can be shown provided a subadditivity condition on the outcome function holds.     

An experimental study of voting rules and polls in three-candidate elections

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.     

Downsian competition with four parties

Our purpose in this article is to study a unidimensional model of spatial electoral competition with four political parties. We assume that the voters are distributed along [0,1] in such a way that the density δ of this distribution is continuous on [0,1] and strictly positive on (0,1). The parties engage in a Downsian competition which is modeled as a non-cooperative four-person game with [0,1] as the common strategy set. If ξ_i stands for the ith quartile of the above-mentioned distribution, then we prove that has a pure Nash equilibrium, if and only if for every t (ξ₁,ξ₃). Moreover, if this condition is satisfied, then has exactly six pure Nash equilibria, which are characterized by the fact that two of the parties put forward the policy that corresponds to ξ₁ and the other two of them put forward the policy that corresponds to ξ₃.     

Stationary and nonstationary strategies in Hotelling's model of spatial competition with repeated pricing decisions

This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary, and there is only one seller in the market in infinitely many periods. Received July 1996/Final version May 1998     

Impatience and dynamic optimal behavior: A bifurcation analysis of the Robinson-Solow-Srinivasan model

This paper provides a study of optimal economic growth under discounting in discrete time in a two-sector version of the Robinson-Solow-Srinivasan model. It examines how dynamic optimal behavior changes in response to increasing impatience. The optimal policy function is a pan map for high discount factors and a check map for low discount factors. It is shown that the transformation from the pan map to the check map, for the intermediate range of discount factors, can be quite intricate. This is demonstrated by proving the existence of two bifurcation values of the discount factor in the borderline case of the model, which establishes the possibility of reswitching of optimal actions as the discount factor varies.     

Information aggregation in multicandidate elections under plurality rule and runoff voting

I consider a model in which imperfectly informed voters with common interests participate in a multicandidate election decided by either plurality rule or a runoff. Prior to the election, each voter receives a private signal corresponding to the candidate the voter thinks is best. Voters are relatively more likely to think a given candidate is best if the candidate is a relatively better candidate. I show that there is a sequence of equilibrium strategies for the voters such that, as the number of voters goes to infinity, the probability that the best candidate is elected goes to 1. I further show that all candidates receive significant vote shares in any equilibrium in which information fully aggregates under plurality rule and that voters do at least as well when the election is decided by a runoff as they do when the election is decided by plurality rule.     

Simple centrifugal incentives in spatial competition

This paper studies the effects of introducing centrifugal incentives in an otherwise standard Downsian model of electoral competition. First, we demonstrate that a symmetric equilibrium is guaranteed to exist when centrifugal incentives are induced by any kind of partial voter participation (such as abstention due to indifference, abstention due to alienation, etc.) and, then, we argue that: (a) this symmetric equilibrium is in pure strategies, and it is hence convergent, only when centrifugal incentives are sufficiently weak on both sides; (b) when centrifugal incentives are strong on both sides (when, for example, a lot of voters abstain when they are sufficiently indifferent between the two candidates) players use mixed strategies—the stronger the centrifugal incentives, the larger the probability weight that players assign to locations near the extremes; and (c) when centrifugal incentives are strong on one side only—say for example only on the right—the support of players’ mixed strategies contain all policies except from those that are sufficiently close to the left extreme.     

Strong and coalition-proof political equilibria under plurality and runoff rule

We analyze the effects of voter coordination on the equilibrium of voting games. Specifically, we analyze the concepts of strong equilibrium and coalition-proof equilibrium for plurality rule and runoff rule elections. We characterize these equilibria in the three candidate case, and provide results for important special cases in the general multicandidate case.      

Asset allocation,sustainable withdrawal,longevity risk and non-exponential discounting

The present paper studies an optimal withdrawal and investment problem for a retiree who is interested in sustaining her retirement consumption above a pre-specified minimum consumption level. Apparently, the withdrawal and investment policy depends substantially on the retiree’s health condition and her time preferences (subjective discount factor). We assume that the health of the retiree can worsen or improve in an unpredictable way over her lifetime and model the retiree’s mortality intensity by a stochastic process. In order to make the decision about the consumption and investment policy more realistic, we assume that the retiree applies a non-exponential discount factor (an exponential discount factor with a small amount of hyperbolic discounting) to value her future income. In other words, we consider an optimization problem by combining four important aspects: asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting. Due to the non-exponential discount factor, we have to solve a time-inconsistent optimization problem. We derive a non-local HJB equation which characterizes the equilibrium optimal investment and consumption strategy. We establish the first-order expansions of the equilibrium value function and the equilibrium strategies by applying expansion techniques. The expansion is performed on the parameter controlling the degree of discounting in the hyperbolic discounting that is added to the exponential discount factors. The first-order equilibrium investment and consumption strategies can be calculated in a feasible way by solving PDEs.     

A mathematical model for estimating the potential margin of state undecided voters for a candidate in a US Federal election

A US Federal election in which candidates from two major political parties compete for the votes of those undecided voters in a state who usually do not vote in US elections is considered. A mathematical model for evaluating the expectation of the margin of votes to be received from such voters by either candidate as a result of the election campaigns of all the competing candidates is proposed. On the basis of this model, finding the estimation under consideration is reducible to finding the minimum of the maximin function of the difference of two bilinear functions with one and the same first vector argument whose second vector arguments belong to a polyhedron of connected variables (strategies of the candidates), and this minimum is sought on another polyhedron.     

Discounted and finitely repeated minority games with public signals

We consider a repeated game where at each stage players simultaneously choose one of the two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. [Renault, J., Scarlatti, S., Scarsini, M., 2005. A folk theorem for minority games. Games Econom. Behav. 53 (2), 208–230], who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.     

A lemma in open sequential voting by veto

The paper is devoted to the investigation of intuitively rational choice in a hierarchical game that is a model of election by open sequential veto-voting. Casting a veto against voter’s least preferred alternative (among remaining ones) may not lead to a sophisticated equilibrium. It means that sincere choice (being intuitive) is not rational. There arises the problem of finding conditions under which a sophisticated optimal sequence of actions is intuitively rational. We prove that in the case of strict preference ordering of alternatives, there exists an intuitively rational sophisticated optimal sequence. In the sequence, each voter vetoes an alternative less preferred than the sophisticated equilibrium outcome. Thus, only intuitively rational strategies are to be considered, although complete information about voters’ preferences is still needed.     

Rational ignorance and voting behavior

We model a two-alternative election in which voters may acquire information about which is the best alternative for all voters. Voters differ in their cost of acquiring information. We show that as the number of voters increases, the fraction of voters who acquire information declines to zero. However, if the support of the cost distribution is not bounded away from zero, there is an equilibrium with some information acquisition for arbitrarily large electorates. This equilibrium dominates in terms of welfare any equilibrium without information acquisition – even though generally there is too little information acquisition with respect to an optimal strategy profile.      

The effective minimax value of asynchronously repeated games

We study the effect of asynchronous choice structure on the possibility of cooperation in repeated strategic situations. We model the strategic situations as asynchronously repeated games, and define two notions of effective minimax value. We show that the order of players moves generally affects the effective minimax value of the asynchronously repeated game in significant ways, but the order of moves becomes irrelevant when the stage game satisfies the non-equivalent utilities (NEU) condition. We then prove the Folk Theorem that a payoff vector can be supported as a subgame perfect equilibrium outcome with correlation device if and only if it dominates the effective minimax value. These results, in particular, imply both Lagunoff and Matsuis (1997) result and Yoon (2001)s result on asynchronously repeated games.I thank three anonymous referees as well as an associate editor for many helpful comments and suggestions. This research was supported by the Suam Foundation Research Grants.Received: October 2001     

随机需求下三度价格歧视重复博弈的研究

基于随机需求函数,讨论了相互竞争的两厂商实施三度价格歧视无限次重复博弈和不定次重复博弈的均衡分析,在三度价格歧视无限次重复博弈分析中,得出了两厂商在贴现因子影响下的子博弈完美纳什均衡.在三度价格歧视不定次重复博弈分析中,设计了不同的方案并进行了Matlab仿真,比较了不同贴现因子下不同仿真方案的厂商得益,并对仿真结果进行了系统分析,得到了统计意义下的均衡分析.     

The geometry of manipulation — A quantitative proof of the Gibbard-Satterthwaite theorem

We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ?? 4 alternatives and n voters will be manipulable with probability at least 10^?4??² n ^?3 q ^?30, where ?? is the minimal statistical distance between f and the family of dictator functions. Our results extend those of [11], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [4,6,9,15,7]) cannot hide manipulations completely. Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies.     

Government formation in a two dimensional policy space

Given any allocation of parliament seats among parties, we characterize all the stable government configurations (supported by at least a majority of the parliament) in terms of winning coalitions and policy outcomes. We consider a two dimensional policy space and we assume that there are four parties that care mainly about holding office, and only instrumentally about policy. We find that for any distribution of seats in the parliament only two scenarios are possible: either there is a party that is a member of almost all equilibrium coalitions (dominant party scenario) or there is a party that is never a member of an equilibrium coalition (dominated party scenario). We characterize the key party for each possible scenario and we show that it is sufficient that the key party has intense preferences over one the issues to guarantee the formation of a stable government coalition.     

Relative impatience determines preference between contract bargaining and repeated bargaining

In this paper we consider the effect of the `impatience ratio' I (of the worker discount factor to the firm discount factor) on the preferences of the players between two bargaining schemes in an asymmetric information wage bargaining context. The firm has private information about the worker's value and the worker makes wage demands. In the contact bargaining scheme, a wage demand which is accepted in one period is binding for all future periods (and hence the bargaining ends after acceptance of a wage demand). In the repeated bargaining scheme, the parties continue to bargain irrespective of whether the worker has been hired or not, and any accepted wage demand is only valid for the period in which it was accepted. We establish the following results under the assumption that the worker's value is uniformly distributed on an interval: When the firm is more patient than the worker (I<1) both parties prefer contract bargaining, and when the worker is more patient than the firm (I >1) both prefer repeated bargaining. For any value of I, the preferred type of bargaining gives the lower unemployment.  The work of Bae has already shown that when players are equally patient (I=1) the players are indifferent between the two schemes, regardless of the distribution of the worker's value. This paper shows that Bae's indifference result (Bae, 1991) cannot be extended to unequally patient players. Received: December 1996/Final version: October 1998