This paper explores whether the addition of costly, imperfect, and exploitable advisors to Berg's investment game enhances or detracts from investor performance in both one-shot and multi-round interactions.We then leverage our findings to develop an automated investor agent that performs as well as or better than humans in these games.To gather this data, we extended Berg's game and conducted a series of experiments using Amazon's Mechanical Turk to determine how humans behave in these potentially adversarial conditions.Our results indicate that, in games of short duration, advisors do not stimulate positive behavior and are not useful in providing actionable advice.In long-term interactions, however, advisors do stimulate positive behavior with significantly increased investments and returns.By modeling human behavior across several hundred participants, we were then able to develop agent strategies that maximized return on investment and performed as well as or significantly better than humans.In one-shot games, we identified an ideal investment value that, on average, resulted in positive returns as long as advisor exploitation was not allowed.For the multi-round games, our agents relied on the corrective presence of advisors to stimulate positive returns on maximum investment.

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.

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.

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.

The VCG mechanism is the standard method to incentivize bidders in combinatorial auctions to bid truthfully. Under the VCG mechanism, the auctioneer can sometimes increase revenue by “burning” items. We study this phenomenon in a setting where items are described by a number of attributes. The value of an attribute corresponds to a quality level, and bidders’ valuations are non-decreasing in the quality levels. In addition to burning items, we allow the auctioneer to present some of the attributes as lower quality than they actually are. We consider the following two revenue maximization problems under VCG: finding an optimal way to mark down items by reducing their quality levels, and finding an optimal set of items to burn. We study the effect of the following parameters on the computational complexity of these two problems: the number of attributes, the number of quality levels per attribute, and the complexity of the bidders’ valuation functions. Bidders have unit demand, so VCG’s outcome can be computed in polynomial time, and the valuation functions we consider are step functions that are non-decreasing with the quality levels. We prove that both problems are NP-hard even in the following three simple settings: a) four attributes, arbitrarily many quality levels per attribute, and single-step valuation functions, b) arbitrarily many attributes, two quality levels per attribute, and single-step valuation functions, and c) one attribute, arbitrarily many quality levels, and multi-step valuation functions. For the case where items have only one attribute, and every bidder has a single-step valuation (zero below some quality threshold), we show that both problems can be solved in polynomial-time using a dynamic programming approach. For this case, we also quantify how much better marking down is than item burning, and we compare the revenue of both approaches with computational experiments.

Most work building on the Stackelberg security games model assumes that the attacker can perfectly observe the defender's randomized assignment of resources to targets. This assumption has been challenged by recent papers, which designed tailor-made algorithms that compute optimal defender strategies for security games with limited surveillance. We analytically demonstrate that in zero-sum security games, lazy defenders, who simply keep optimizing against perfectly informed attackers, are almost optimal against diligent attackers, who go to the effort of gathering a reasonable number of observations. This result implies that, in some realistic situations, limited surveillance may not need to be explicitly addressed.

In the Real-Time Agent-Centered Search (RTACS) problem,an agent has to arrive at a goal location while acting and reasoningin the physical world. Traditionally, RTACS problemsare solved by propagating and updating heuristic values ofstates visited by the agent. In existing RTACS algorithms theagent may revisit each state many times causing the entireprocedure to be quadratic in the state space. We study theIterative Deepening (ID) approach for solving RTACS andintroduce Exponential Deepening A* (EDA*), an RTACS algorithmwhere the threshold between successive Depth-Firstcalls is increased exponentially. EDA* is proven to hold aworst case bound that is linear in the state space. Experimentalresults supporting this bound are presented and demonstrateup to 10x reduction over existing RTACS solvers wrtdistance traveled, states expanded and CPU runtime.

The Fisher market model is one of the most fundamental resource allocation models in economics. In a Fisher market, the prices and allocations of goods are determined according to the preferences and budgets of buyers to clear the market. In a Fisher market game, however, buyers are strategic and report their preferences over goods; the market-clearing prices and allocations are then determined based on their reported preferences rather than their real preferences. We show that the Fisher market game always has a pure Nash equilibrium, for buyers with linear, Leontief, and Cobb-Douglas utility functions, which are three representative classes of utility functions in the important Constant Elasticity of Substitution (CES) family. Furthermore, to quantify the social efficiency, we prove Price of Anarchy bounds for the game when the utility functions of buyers fall into these three classes respectively.

We consider settings where a collective intelligence is formed by aggregating information contributed from many independent agents, such as product reviews, community sensing, or opinion polls. We propose a novel mechanism that elicits both private signals and beliefs. The mechanism extends the previous versions of the Bayesian Truth Serum (the original BTS, the RBTS, and the multi-valued BTS), by allowing small populations and non-binary private signals, while not requiring additional assumptions on the belief updating process. For priors that are sufficiently smooth, such as Gaussians, the mechanism allows signals to be continuous.

Agency - the capacity to plan and act - and experience - the capacity to sense and feel - are two critical aspects that determine whether people will perceive non-human entities, such as autonomous agents, to have a mind. There is evidence that the absence of either can reduce cooperation. We present an experiment that tests the necessity of both for cooperation with agents. In this experiment we manipulated people's perceptions about the cognitive and affective abilities of agents, when engaging in the ultimatum game. The results indicated that people offered more money to agents that were perceived to make decisions according to their intentions (high agency), rather than randomly (low agency). Additionally, the results showed that people offered more money to agents that expressed emotion (high experience), when compared to agents that did not (low experience). We discuss the implications of this agency-experience theoretical framework for the design of artificially intelligent decision makers.