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 -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.

Crowdsourcing offers unprecedented potential for solving tasks efficiently by tapping into the skills of large groups of people. A salient feature of crowdsourcing-its openness of entry-makes it vulnerable to malicious behaviour. Such behaviour took place in a number of recent popular crowdsourcing competitions. We provide game-theoretic analysis of a fundamental trade-off between the potential for increased productivity and the possibility of being set back by malicious behaviour. Our results show that in crowdsourcing competitions malicious behaviour is the norm, not the anomaly-a result contrary to the conventional wisdom in the area. Counterintuitively, making the attacks more costly does not deter them but leads to a less desirable outcome. These findings have cautionary implications for the design of crowdsourcing competitions.

No abstract

Abstract. Redistribution of VCG payments has been mostly studied in the context of resource allocation. This paper focuses on another fundamental model-the public project problem. In this scenario, the VCG mechanism collects in payments up to n−1 n of the total value of the agents. This collected revenue represents a loss of social welfare. Given this, we study how to redistribute most of the VCG revenue back to the agents. Our first result is a bound on the best possible efficiency ratio, which we conjecture to be tight based on numerical simulations. Furthermore, the upper bound is confirmed on the case with 3 agents, for which we derive an optimal redistribution function. For more than 3 agents, we turn to heuristic solutions and propose a new approach to designing redistribution mechanisms.

Online social networks offer unprecedented potential for rallying a large number of people to accomplish a given task. Here we focus on information gathering tasks where rare information is sought through “referral-based crowdsourcing”: the information request is propagated recursively through invitations among members of a social network. Whereas previous work analyzed incentives for the referral process in a setting with only correct reports, misreporting is known to be both pervasive in crowdsourcing applications, and difficult/costly to filter out. A motivating example for our work is the DARPA Red Balloon Challenge where the level of misreporting was very high. In order to undertake a formal study of verification, we introduce a model where agents can exert costly effort to perform verification and false reports can be penalized. This is the first model of verification and it provides many directions for future research, which we point out. Our main theoretical result is the compensation scheme that minimizes the cost of retrieving the correct answer. Notably, this optimal compensation scheme coincides with the winning strategy of the Red Balloon Challenge.