Strategy-Proofness and Single-Crossing

This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n - 1 fixed ballots located at the end points of the set of alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. And it offers a strategic foundation for the so called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.Strategy-proofness; single-crossing; median voter; positional dictators

On the existence of Nash equilibrium in electoral competition

This paper generalizes previous existence results on unidimensional electoral competition, by extending the traditional two-party electoral game to the case where parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. Although this game has discontinuous payoffs, it satisfies payoff security and reciprocally upper semi- continuity. However, conditional payoffs might violate quasi-concavity. Hence, our first result shows that the existence of a pure-strategy Nash equilibrium can be guaranteed only if parties' interests are symmetric. Instead, we prove that the mixed extension satisfies better reply security and, therefore, that a mixed-strategy equilibrium always exists. We also characterize the set of equilibria for a tractable version of the model. This shows that the interaction between the electoral uncertainty, the aggregate level of opportunism and its distribution among parties shape the equilibrium strategies. In particular, when the opportunism is large and asymmetrically distributed, the support of each mixed-strategy equilibrium is a closed interval located on one side of the median. Further, as the uncertainty increases, the probability distributions concentrate on the extremes of the support. And the mixed-strategy equilibrium vanishes above a critical level, over which each party plays a pure strategy in its own ideological side.Electoral competition, mixed motivations, discontinuous games, Nash equilibrium.

Existence and uniqueness of Nash equilibrium in electoral competition games: The hybrid case

This paper analyzes the traditional unidimensional, two-party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game, refer to as the hybrid election game, is shown to be payoff secure and reciprocally upper semi-continuous. Conditional payoffs, however, are not quasi-concave. Hence, the existence of a pure strategy Nash equilibrium (PSNE) is ensured only if parties have homogenous interests in power. In that case, an equilibrium not only exists, but it is also unique. Instead, if parties have heterogeneous motivations, depending upon the relationship between the electoral uncertainty, the aggregate opportunism and its distribution across parties, a psne may or may not exist. The mixed extension, however, is always better reply secure. Therefore, a mixed strategy Nash equilibrium do indeed exist. These results generalize previous existence results in unidimensional electoral competition.Electoral competition; mixed motivations; discontinuous games; Nash equilibrium.

Bertrand's price competition in markets with fixed costs

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly break-even price, denoted by D(pL (n)), is sufficient to guarantee that the market supports a (not necessarily symmetric) Bertrand equilibrium in pure strategies with two or more firms supplying at least D(pL (n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(p(n)).Bertrand competition, cost subadditivity, fixed costs, natural monopoly.

Single-Crossing, Strategic Voting and the Median Choice Rule

This paper studies the strategic foundations of the Representative Voter Theorem (Rothstein, 1991), also called the "second version" of the Median Voter Theorem. As a by-product, it also considers the existence of non-trivial strategy-proof social choice functions over the domain of single-crossing preference profiles. The main result presented here is that single-crossing preferences constitute a domain restriction on the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median choice rule, which is found to be strategy-proof and group-strategic-proof not only over the full set of alternatives, but also over every possible policy agenda. The paper also shows the close relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median choice rule to prove that the collective outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism in which, first, individuals select a representative among themselves, and then the representative voter chooses a policy to be implemented by the planner.Single-crossing; order-restriction; median voter; strategyproofness.

Bertrand's price competition in markets with fixed costs

We analyze Bertrand's price competition in a homogenous good market with a fixed cost and an increasing marginal cost (i.e., with variable returns to scale). If the fixed cost is avoidable, we show that the non-subadditivity of the cost function at the output corresponding to the oligopoly break-even price, denoted by D(pL(n)), is su±cient to guarantee that the market supports an equilibrium in pure strategies with two or more active firms supplying at least D(pL(n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(pL(n)). As a by-product, the latter implies that the average cost cannot be decreasing over the range of outputs mentioned before. In addition, we also prove that the existence of a price-taking equilibrium is sufficient, but not necessary, for Bertrand's price competition to possess an equilibrium in pure strategies. This provides a simple existence result for the case where the fixed cost is fully unavoidable.

Separation of Powers and Political Budget Cycles

From a theoretical viewpoint, political budget cycles (PBC) arise in equilibrium when rational voters are imperfectly informed about the incumbent's competency and the incumbent enjoys discretionary power over the budget. This paper focuses on the second condition, examining how executive discretion is affected by the budgetary process under separation of powers. We specifically model PBC in the composition of government spending. The main result is that effective checks and balances in the budgetary process curb PBC. The institutional features of the executive-legislature bargaining game, namely, the actual agenda-setting authority, the status quo location and the degree of legislative oversight and control of the implementation of the budgetary law, play critical roles for the existence and the size of PBC. These results are consistent with recent empirical findings, which show that PBC are more pronounced in developing countries, where there are also less effective checks and balances.Rational political budget cycles; budget composition; separation of powers; checks and balances; budgetary process.

Political Motivations and Electoral Competition: Equilibrium Analysis and Experimental Evidence

We study both theoretically and experimentally the complete set of Nash equilibria of a classical one-dimensional, majority rule election game with two candidates, who might be interested in power as well as in ideology, but not necessarily in the same way. Apart from obtaining the well known median voter result and the two-sided policy differentiation outcome, the paper uncovers the existence of two new equilibrium configurations, called 'one-sided' and 'probabilistic' policy differentiation, respectively. Our analysis shows how these equilibrium configurations depend on the relative interests in power (resp., ideology) and the uncertainty about voters' preferences. The theoretical predictions are supported by the data collected from a series of laboratory experiments, as we observe convergence to the Nash equilibrium values at the aggregate as well as the individual levels in all treatments, and the comparative statics effects across treatments are as predicted by the theory.Electoral competition, Power, Ideology, Uncertainty, Nash equilibrium, Experimental evidence

Single-crossing, strategic voting and the median choice rule

This paper studies the strategic foundations of the Representative Voter Theorem (Rothstein, 1991), also called the second version of the Median Voter Theorem. As a by-product, it also considers the existence of non-trivial strategy-proof social choice functions over the domain of single-crossing preference profiles. The main result presented here is that single-crossing preferences constitute a domain restriction on the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median choice rule, which is found to be strategy-proof and group-strategic-proof not only over the full set of alternatives, but also over every possible policy agenda. The paper also shows the close relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median choice rule to prove that the collective outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism in which, first, individuals select a representative among themselves, and then the representative voter chooses a policy to be implemented by the planner

Redistribution, power sharing and inequality concern

From Springer Nature via Jisc Publications RouterHistory: received 2017-12-30, registration 2021-01-27, accepted 2021-01-27, pub-electronic 2021-03-10, online 2021-03-10, pub-print 2021-08Publication status: PublishedAbstract: We analyze a political competition model of redistributive policies. We provide an equilibrium existence result and a full characterization of the net transfers to the different income groups. We also derive several testable predictions about the way in which the net group transfers and the after-tax Gini coefficient vary with the main parameters of the model. In accordance with the theory, the empirical evidence from a sample of developed and developing democracies supports a highly statistically significant association between: (i) the net group transfer and the gap between the population and the group mean initial income, and (ii) the net group transfer (and resp., the Gini coefficient) and power sharing disproportionality. In addition, the data also provide some empirical evidence confirming a significant relationship between the net transfers to the poor (and resp., the Gini) and the concern of the political parties with income inequality