Robert J. Weber

A theory of auctions and competitive bidding

Abstract : In Section 2, we review some important results of the received auction theory, introduce a new general auction model, and summarize the results of our analysis. Section 3 contains a formal statement of our model, and develops the properties of affiliated random variables. The various theorems are presented in Sections 4-8. In Section 9, we offer our views on the current state of auction theory. Following Section 9 is a technical appendix dealing with affiliated random variables.

Distributional Strategies for Games with Incomplete Information

We study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game-theoretic models. Using the notion of “distributional” strategies, we prove four main theorems: (i) a mixed-strategy Nash equilibrium existence theorem, (ii) a pure-strategy equilibrium existence theorem, (iii) a pure-strategy (epsilon)-equilibrium existence theorem, and (iv) a theorem describing how the set of equilibria of a game varies with the parameters of the game.

Probabilistic Values for Games

Abstract : Much attention has been given to methods for measuring the value of playing a particular role in a n-person game. The study of various values is motivated by several considerations. One is to determine an equitable distribution of the wealth available to the players through their participation in the game. Another is to help an individual compare his prospects from participation in several games. A study of equitable distributions may shed light upon a players prospects. However, a study of individual prospects need not yield any information concerning the relative fairness of various distributions of wealth.

A Theory of Voting Equilibria

A voting equilibrium arises when the voters in an electorate, acting in accordance with both their preferences for the candidates and their perceptions of the relative chances of various pairs of candidates being in contention for victory, generate an election result that justifies their perceptions. Voting equilibria always exist, and the set of equilibria can vary substantially with the choice of voting system. We compare equilibria under the plurality rule, approval voting, and the Borda system. We consider a candidate-positioning game and find that the plurality rule imposes little restriction on the position of the winning candidate in three-candidate races, while approval voting leads to a winner positioned at the median of the voter distribution. We contrast campaign activities intended to influence voter preferences with activities meant to influence only perceptions of candidate viability.

Competitive Bidding and Proprietary Information

The auction of an object is considered, for the case in which one bidder is better-informed than the others concerning the actual value of the object. An equilibrium point solution of the competitive bidding game is determined; at this equilibrium, the expected revenue of the less-well-informed bidders is zero. The case of an object which can take only values from a discrete set is dealt with as the limit of auctions of continuously-valued objects.

Value Theory Without Efficiency

A semivalue is a symmetric positive linear operator on a space of games, which leaves the additive games fixed. Such an operator satisfies all of the axioms defining the Shapley value, with the possible exception of the efficiency axiom. The class of semivalues is completely characterized for the space of finite-player games, and for the space pNA of nonatomic games.

An Experiment on Coordination in Multi-Candidate Elections: The Importance of Polls and Election Histories

Do polls simply measure intended voter behavior or can they affect it and, thus, change election outcomes? Do candidate ballot positions or the results of previous elections affect voter behavior? We conduct several series of experimental, three-candidate elections and use the data to provide answers to these questions. In these elections, we pay subjects conditionally on election outcomes to create electorates with publicly known preferences. A majority (but less than two-thirds) of the voters are split in their preferences between two similar candidates, while a minority (but plurality) favor a third, dissimilar candidate. If all voters voted sincerely, the third candidate — a Condorcet loser — would win the elections. We find that pre-election polls significantly reduce the frequency with which the Condorcet loser wins. Further, the winning candidate is usually the majority candidate who is listed first on the poll and election ballots. The evidence also shows that a shared history enables majority voters to coordinate on one of their favored candidates in sequences of identical elections. With polls, majority-preferred candidates often alternate as election winners.

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. Duvergers 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.

A sequential auction involving asymmetrically-informed bidders

An example is given of a sequential auction in which, at equilibrium, the expected profit of an informed bidder may be strictly less than the expected profit of an uninformed bidder. This phenomenon is interpreted in terms of the internal game between a players “types” which arises in a setting of incomplete information.

Campaign Finance Levels as Coordinating Signals in Three-Way, Experimental Elections

If (often costly) election campaigns are simply advertising, they do not increase social welfare directly. Given this, should we limit campaign expenditures? We propose that costly campaigns can inform voters about the strength of candidates. This may increase welfare indirectly by helping voters avoid coordination failures. In laboratory elections, we study campaign finance levels as coordinating signals and compare them with our earlier work on polls. Both coordinate majority voters effectively, allowing them to stop Condorcet losers from winning. Finance levels were rational in that the total benefits of coordination exceeded the costs. Further, benefits of typical incremental contributions exceeded costs ex-post, while the next typical increments benefits would not have.