We investigate the limiting behavior of trader wealth and prices in a simple prediction market with a finite set of participants having heterogeneous beliefs. Traders bet repeatedly on the outcome of a binary event with fixed Bernoulli success probability. A class of strategies, including (fractional) Kelly betting and constant relative risk aversion (CRRA) are considered. We show that when traders are willing to risk only a small fraction of their wealth in any period, belief heterogeneity can persist indefinitely; if bets are large in proportion to wealth then only the most accurate belief type survives. The market price is more accurate in the long run when traders with less accurate beliefs also survive. That is, the survival of traders with heterogeneous beliefs, some less accurate than others, allows the market price to better reflect the objective probability of the event in the long run.

We study the envy-free allocation of indivisible goods between two players. Our novel setting includes an option to sell each good for a fraction of the minimum value any player has for the good. To rigorously quantify the efficiency gain from selling, we reason about the price of envy-freeness of allocations of sellable goods — the ratio between the maximum social welfare and the social welfare of the best envy-free allocation. We show that envy-free allocations of sellable goods are significantly more efficient than their unsellable counterparts.

Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of scores obtained from the votes. This defines a new family of voting rules, rank-dependent scoring rules (RDSRs), based on ordered weighted average (OWA) operators, which, include all scoring rules, and many others, most of which of new. We study some properties of these rules, and show, empirically, that certain RDSRs are less manipulable than Borda voting, across a variety of statistical cultures.

Mobile geo-location advertising, where mobile ads are targeted based on a user’s location, has been identified as a key growth factor for the mobile market. As with online advertising, a crucial ingredient for their success is the development of effective economic mechanisms. An important difference is that mobile ads are shown sequentially over time and information about the user can be learned based on their movements. Furthermore, ads need to be shown selectively to prevent ad fatigue. To this end, we introduce, for the first time, a user model and suitable economic mechanisms which take these factors into account. Specifically, we design two truthful mechanisms which produce an advertisement plan based on the user’s movements. One mechanism is allocatively efficient, but requires exponential compute time in the worst case. The other requires polynomial time, but is not allocatively efficient. Finally, we experimentally evaluate the trade off between compute time and efficiency of our mechanisms.

There is often a large disparity between the size of a game we wish to solve and the size of the largest instances solvable by the best algorithms; for example, a popular variant of poker has about $10^{165}$ nodes in its game tree, while the currently best approximate equilibrium-finding algorithms scale to games with around $10^{12}$ nodes. In order to approximate equilibrium strategies in these games, the leading approach is to create a sufficiently small strategic approximation of the full game, called an abstraction, and to solve that smaller game instead. The leading abstraction algorithm for imperfect-information games generates abstractions that have imperfect recall and are distribution aware, using $k$-means with the earth mover's distance metric to cluster similar states together. A distribution-aware abstraction groups states together at a given round if their full distributions over future strength are similar (as opposed to, for example, just the expectation of their strength). The leading algorithm considers distributions over future strength at the final round of the game. However, one might benefit by considering the trajectory of distributions over strength in all future rounds, not just the final round. An abstraction algorithm that takes all future rounds into account is called potential aware. We present the first algorithm for computing potential-aware imperfect-recall abstractions using earth mover's distance. Experiments on no-limit Texas Hold'em show that our algorithm improves performance over the previously best approach.

Examples range from multiagent planning, That is, we look for the most representative voter and return to crowdsourcing and human computation, to collaborative her ballot as the outcome. In our example, a natural choice filtering for recommender systems, to rank aggregation would be any of the voters voting (0, 1, 1). The distance of for search engines, to coordination and resource allocation this choice to the individual ballots is 42 (21 voters disagree in multiagent systems. Several frameworks have been on 2 issues each), i.e., this solution is only marginally worse proposed in the literature on computational social choice than the solution returned by the distance-based rule--and it (Chevaleyre et al. 2007; Brandt, Conitzer, and Endriss 2013) is optimal in case (1, 1, 1) is infeasible.

Structured preference domains, such as, for example, the domains of single-peaked and single-crossing preferences, are known to admit efficient algorithms for many problems in computational social choice. Some of these algorithms extend to preferences that are close to having the respective structural property, i.e., can be made to enjoy this property by performing minor changes to voters' preferences, such as deleting a small number of voters or candidates. However, it has recently been shown that finding the optimal number of voters or candidates to delete in order to achieve the desired structural property is NP-hard for many such domains. In this paper, we show that these problems admit efficient approximation algorithms. Our results apply to all domains that can be characterized in terms of forbidden configurations; this includes, in particular, single-peaked and single-crossing elections. For a large range of scenarios, our approximation results are optimal under a plausible complexity-theoretic assumption. We also provide parameterized complexity results for this class of problems.

While stable matching problems are widely studied, little work has investigated schemes for effectively eliciting agent preferences using either preference (e.g., comparison) queries for interviews (to form such comparisons); and no work has addressed how to combine both. We develop a new model for representing and assessing agent preferences that accommodates both forms of information and (heuristically) minimizes the number of queries and interviews required to determine a stable matching. Our Refine-then-Interview (RtI) scheme uses coarse preference queries to refine knowledge of agent preferences and relies on interviews only to assess comparisons of relatively “close” options. Empirical results show that RtI compares favorably to a recent pure interview minimization algorithm, and that the number of interviews it requires is generally independent of the size of the market.

Extensive-form games are a powerful tool for representing complex multi-agent interactions. Nash equilibrium strategies are commonly used as a solution concept for extensive-form games, but many games are too large for the computation of Nash equilibria to be tractable. In these large games, exploitability has traditionally been used to measure deviation from Nash equilibrium, and thus strategies are aimed to achieve minimal exploitability. However, while exploitability measures a strategy's worst-case performance, it fails to capture how likely that worst-case is to be observed in practice. In fact, empirical evidence has shown that a less exploitable strategy can perform worse than a more exploitable strategy in one-on-one play against a variety of opponents. In this work, we propose a class of response functions that can be used to measure the strength of a strategy. We prove that standard no-regret algorithms can be used to learn optimal strategies for a scenario where the opponent uses one of these response functions. We demonstrate the effectiveness of this technique in Leduc Hold'em against opponents that use the UCT Monte Carlo tree search algorithm.

We study the problem where a task (or multiple unrelated tasks) must be executed, there are multiple machines/agents that can potentially perform the task, and our objective is to minimize the expected sum of the agents' processing times. Each agent does not know exactly how long it will take him to finish the task; he only knows the distribution from which this time is drawn. These times are independent across agents and the distributions fulfill the monotone hazard rate condition. Agents are selfish and will lie about their distributions if this increases their expected utility. We study different variations of the Vickrey mechanism that take as input the agents' reported distributions and the players' realized running times and that output a schedule that minimizes the expected sum of processing times, as well as payments that make it an ex-post equilibrium for the agents to both truthfully report their distributions and exert full effort to complete the task. We devise the ChPE mechanism, which is uniquely tailored to our problem, and has many desirable properties including: not rewarding agents that fail to finish the task and having non-negative payments.