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Empirical Analysis of Plurality Election Equilibria
, 2013
"... Voting is widely used to aggregate the different preferences of agents, even though these agents are often able to manipulate the outcome through strategic voting. Most research on manipulation of voting methods studies (1) limited solution concepts, (2) limited preferences, or (3) scenarios with a ..."
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Cited by 7 (2 self)
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Voting is widely used to aggregate the different preferences of agents, even though these agents are often able to manipulate the outcome through strategic voting. Most research on manipulation of voting methods studies (1) limited solution concepts, (2) limited preferences, or (3) scenarios with a few manipulators that have a common goal. In contrast, we study voting in plurality elections through the lens of Nash equilibrium, which allows for the possibility that any number of agents, with arbitrary different goals, could all be manipulators. This is possible thanks to recent advances in (Bayes-)Nash equilibrium computation for large games. Although plurality has numerous pure-strategy Nash equilibria, we demonstrate how a simple equilibrium refinement— assuming that agents only deviate from truthfulness when it will change the outcome—dramatically reduces this set. We also use symmetric Bayes-Nash equilibria to investigate the case where voters are uncertain of each others ’ preferences. This refinement does not completely eliminate the problem of multiple equilibria. However, it does show that even when agents manipulate, plurality still tends to lead to good outcomes (e.g., Condorcet winners, candidates that would win if voters were truthful, outcomes with high social welfare).
Exploiting structure in cooperative Bayesian games
- In UAI
, 2012
"... Cooperative Bayesian games (BGs) can model decision-making problems for teams of agents under imperfect information, but require space and computation time that is exponential in the number of agents. While agent independence has been used to mitigate these problems in perfect information settings, ..."
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Cited by 7 (7 self)
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Cooperative Bayesian games (BGs) can model decision-making problems for teams of agents under imperfect information, but require space and computation time that is exponential in the number of agents. While agent independence has been used to mitigate these problems in perfect information settings, we propose a novel approach for BGs based on the observation that BGs additionally possess a different types of structure, which we call type independence. We propose a factor graph representation that captures both forms of independence and present a theoretical analysis showing that non-serial dynamic programming cannot effectively exploit type independence, while Max-Sum can. Experimental results demonstrate that ourapproachcantacklecooperativeBayesian games of unprecedented size. 1
Empirical Aspects of Plurality Election Equilibria
"... Social choice functions aggregate the different preferences of agents, choosing from a set of alternatives. Most research on manipulation of voting methods studies (1) limited solution concepts, (2) limited preferences, or (3) scenarios with a few manipulators that have a common goal. In contrast, w ..."
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Cited by 1 (1 self)
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Social choice functions aggregate the different preferences of agents, choosing from a set of alternatives. Most research on manipulation of voting methods studies (1) limited solution concepts, (2) limited preferences, or (3) scenarios with a few manipulators that have a common goal. In contrast, we study voting in plural-ity elections through the lens of Nash equilibrium, which allows for the possibility that any number of agents, with arbitrary different goals, could all be manipula-tors. We do this through a computational analysis, leveraging recent advances in (Bayes-)Nash equilibrium computation for large games. Although plurality has ex-ponentially many pure-strategy Nash equilibria, we demonstrate how a simple equi-librium refinement—assuming that agents very weakly prefer to vote truthfully— dramatically reduces this set. We also use symmetric Bayes-Nash equilibria to in-vestigate the case where voters are uncertain of each others ’ preferences. Although our refinement does not completely eliminate the problem of multiple equilibria, it tends to predict an increased probability that a good candidate will be selected (e.g., the candidate that would win if voters were truthful, or a Condorcet winner). 1
Virtual Integration -- A Game-Theoretic Approach
, 2014
"... Embedded systems are playing a key role to enable the features of todays cars and other road vehicles. Advances in current hardware platforms of these embedded systems and growing implementation of features in software rather than in new hardware modules lead to new and continuously more complex aut ..."
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Embedded systems are playing a key role to enable the features of todays cars and other road vehicles. Advances in current hardware platforms of these embedded systems and growing implementation of features in software rather than in new hardware modules lead to new and continuously more complex automotive software systems. The integration process in the course of development of automotive software systems is a crucial and complex phase. An efficient combination of the set of components into a functioning whole is made difficult due to the fine granular and highly interconnected architectural structure of these systems. Also, the high cost pressure and strict safety requirements in the industry have strong impact on the integration phase. Virtual integration is a proposed methodology, which aims to carry out integration-related activities at an early stage of development. This reduces the pressure during the integration phase and improves the qual-
Individual Planning in Agent Populations: Exploiting Anonymity and
"... Interactive partially observable Markov decision processes (I-POMDP) provide a formal framework for planning for a self-interested agent in multiagent settings. An agent oper-ating in a multiagent environment must deliberate about the actions that other agents may take and the effect these actions h ..."
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Interactive partially observable Markov decision processes (I-POMDP) provide a formal framework for planning for a self-interested agent in multiagent settings. An agent oper-ating in a multiagent environment must deliberate about the actions that other agents may take and the effect these actions have on the environment and the rewards it receives. Tradi-tional I-POMDPs model this dependence on the actions of other agents using joint action and model spaces. Therefore, the solution complexity grows exponentially with the num-ber of agents thereby complicating scalability. In this paper, we model and extend anonymity and context-specific indepen-dence – problem structures often present in agent populations – for computational gain. We empirically demonstrate the effi-ciency from exploiting these problem structures by solving a new multiagent problem involving more than 1,000 agents.
Computing Pure Bayesian-Nash Equilibria in Games with Finite Actions and Continuous Types
, 2013
"... We extend the well-known fictitious play (FP) algorithm to compute pure-strategy Bayesian-Nash equilibria in private-value games of incomplete information with finite actions and continuous types (G-FACTs). We prove that, if the frequency distribution of actions (fictitious play beliefs) converges, ..."
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We extend the well-known fictitious play (FP) algorithm to compute pure-strategy Bayesian-Nash equilibria in private-value games of incomplete information with finite actions and continuous types (G-FACTs). We prove that, if the frequency distribution of actions (fictitious play beliefs) converges, then there exists a pure-strategy equilibrium strategy that is consistent with it. We furthermore develop an algorithm to convert the converged distribution of actions into an equilibrium strategy for a wide class of games where utility functions are linear in type. This algorithm can also be used to compute pure ǫ-Nash equilibria when distributions are not fully converged. We then apply our algorithm to find equilibria in an important and previously unsolved game: simultaneous sealed-bid, second-price auctions where various types of items (e.g., substitutes or complements) are sold. Finally, we provide an analytical characterization of equilibria in games with linear utilities. Specifically, we show how equilibria can be found by solving a system of polynomial equations. For a special case of simultaneous auctions, we also solve the equations confirming the results obtained numerically.
Exploiting Agent and Type Independence in Collaborative Graphical Bayesian Games
, 2011
"... ar ..."
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Price of Anarchy for Auction Revenue
, 2014
"... This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates the standard smoothness framework [e.g., 16] into ..."
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This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates the standard smoothness framework [e.g., 16] into two distinct parts. The first part, value covering, employs best-response analysis to individually relate each agent’s expected price for allocation and welfare in any Bayes-Nash equilibrium. The second part, revenue covering, uses properties of an auction’s rules and feasibility constraints to relate the revenue of the auction to the agents’ expected prices for allocation (not necessarily in equilibrium). Because value covering holds for any equilibrium, proving an auction is revenue covered is a sufficient condition for approximating optimal welfare, and under the right conditions, the optimal revenue. In mechanisms with reserve prices, our welfare results show approximation with respect to the optimal mechanism with the same reserves. As a center-piece result, we analyze the single-item first-price auction with individual monopoly reserves (the price that a monopolist would post to sell to that agent alone, these reserves are generally distinct for agents with values drawn from distinct distributions). When each distribution satisfies the regularity condition of Myerson[13]theauction’srevenue is atleast a 2e e−1 ≈ 3.16approximationto the revenue of the optimal auction revenue. We also give bounds for matroid auctionswithfirstpriceorall-pay semantics, and the generalized first price position auction. Finally, we give an extension theorem for simultaneous composition, i.e., when multiple auctions are run simultaneously, with single-valued and unit demand agents. We thank Vasilis Syrgkanis for comments on a prior version of this paper for which simultaneous composition did not hold, suggesting study of the simultaneous composition setting and for perspective on price-of-anarchy methodology.
