Empirical Game-Theoretic Analysis: A Survey

In the empirical approach to game-theoretic analysis (EGTA), the model of the game comes not from declarative representation, but is derived by interrogation of a procedural description of the game environment. The motivation for developing this approach was to enable game-theoretic reasoning about strategic situations too complex for analytic specification and solution. Since its introduction over twenty years ago, EGTA has been applied to a wide range of multiagent domains, from auctions and markets to recreational games to cyber-security. We survey the extensive methodology developed for EGTA over the years, organized by the elemental subproblems comprising the EGTA process. We describe key EGTA concepts and techniques, and the questions at the frontier of EGTA research. Recent advances in machine learning have accelerated progress in EGTA, and promise to significantly expand our capacities for reasoning about complex game situations.Comment: 72 pages, 17 figure

Bounds and dynamics for empirical game theoretic analysis

This paper provides several theoretical results for empirical game theory. Specifically, we introduce bounds for empirical game theoretical analysis of complex multi-agent interactions. In doing so we provide insights in the empirical meta game showing that a Nash equilibrium of the estimated meta-game is an approximate Nash equilibrium of the true underlying meta-game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the evolutionary dynamics analysis of meta-games using heuristic payoff tables (HPTs) to asymmetric games. The state-of-the-art has only considered evolutionary dynamics of symmetric HPTs in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), the dynamics of several teams of players in the capture the flag game (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the policy-space response oracle multi-agent learning algorithm

A Generalised Method for Empirical Game Theoretic Analysis

This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash equilibrium of the true underlying game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the meta-game analysis methodology to asymmetric games. The state-of-the-art has only considered empirical games in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the PSRO multi-agent learning algorithm.Comment: will appear at AAMAS'1

Scaling Empirical Game-Theoretic Analysis.

To analyze the incentive structure of strategic multi-agent interactions, such scenarios are often cast as games, where players optimize their payoffs by selecting a strategy in anticipation of the strategic decisions of other players. When our modeling needs are too complex to address analytically, empirical game models, game models in which observations of simulated play are used to estimate payoffs of agents, can be employed to facilitate game-theoretic analysis. This dissertation focuses on extending the capability of the empirical game-theoretic analysis (EGTA) framework for modeling and analyzing large games. My contributions are in three distinct areas: increasing the scale of game simulation through software infrastructure, improving performance of common analytic tasks by bringing them closer to the data, and reducing sampling requirements for statistically confident analysis through sequential sampling algorithms. With the advent of EGTAOnline, an experiment management system for distributed game simulation that I developed, EGTA practitioners no longer limit their studies to what can be conducted on a single computer. Over one billion payoff observations have been added to EGTAOnline's database to date, corresponding to hundreds of distinct experiments. To reduce the cost of analyzing this data, I explored conducting analysis in the database. I found that translating data to an in-memory object representation was a dominant cost for game-theoretic analysis software. By avoiding that cost, conducting analysis in the database improves performance. A further way to improve scalability is to ensure we only gather as much data as is necessary to support analysis. I developed algorithms that interweave sampling and evaluations of statistical confidence, improving on existing ad hoc sampling methods by providing a measure of statistical confidence for analysis and reducing the number of observations taken. In addition to these software and methodological contributions, I present two applications: a strategic analysis of selecting a wireless access point for your traffic, and an investigation of mapping an analytical pricing model to a large simulated stock market.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110315/1/bcassell_1.pd

Commitments by Hostage Posting

We survey research on incurring commitments by voluntary hostage posting as a mechanism of cooperation. The Trust Game is employed as a paradigmatic example of cooperation problems. We sketch a very simple game-theoretic model that shows how voluntary hostage posting can bind the trustee and thus induce trustfulness of the trustor as well as trustworthiness of the trustee. We then indicate how the model can be improved by including uncertainty and incomplete information, transaction costs of hostage posting and compensating effects as well as signaling effects of hostages. Further extensions of the theoretical analysis are outlined as well as testable hypotheses and references to empirical research. Problems for future research are suggested.commitments, voluntary hostage posting, trust game

Understanding Financial Market Behavior through Empirical Game-Theoretic Analysis

Financial market activity is increasingly controlled by algorithms, interacting through electronic markets. Unprecedented information response times, autonomous operation, use of machine learning and other adaptive techniques, and ability to proliferate novel strategies at scale are all reasons to question whether algorithmic trading may produce dynamic behavior qualitatively different from what arises in trading under direct human control. Given the high level of competition between trading firms and the significant financial incentives to trading, it is desirable to understand the effect incentives have on the behavior of agents in financial markets. One natural way to analyze this effect is through the economic concept of a Nash equilibrium, a behavior profile of every agent such that no individual stands to gain by doing something different. Some of the incentives traders face arise from the complexities of modern market structure. Recent studies have turned to agent-based modeling as a way to capture behavioral response to this structure. Agent-based modeling is a simulation paradigm that allows studying the interaction of agents in a simulated environment, and it has been used to model various aspects of financial market structure. This thesis builds on recent agent-based models of financial markets by imposing agent rationality and studying the models in equilibrium. I use empirical game-theoretic analysis, a methodology for computing approximately rational behavior in agent-based models, to investigate three important aspects of market structure. First, I evaluate the impact of strategic bid shading on agent welfare. Bid shading is when agents demand better prices, lower if they are buying or higher if they are selling, and is typically associated with lower social welfare. My results indicate that in many market environments, strategic bid shading actually improves social welfare, even with some of the complexities of financial markets. Next, I investigate the optimal clearing interval for a proposed market mechanism, the frequent call market. There is significant evidence to support the idea that traders will benefit from trading in a frequent call market over standard continuous double auction markets. My results confirm this statement for a wide variety of market settings, but I also find a few circumstances, particularly when large informational advantages exist, or when markets are thin, that call markets consistently hurt welfare, independent of frequency. I conclude with an investigation on the effect of trend following on market stability. Here I find that the presence of trend followers alters a market’s response to shock. In the absence of trend followers, shocks are small but have a long recovery. When trend followers are present, they alter background trader behavior resulting in more severe shocks that recover much more quickly. I also develop a novel method to efficiently evaluate the effect of shock anticipation on equilibrium. While anticipation of shocks does make markets more stable, trend followers continue to be profitable.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144031/1/ebrink_1.pd

Defensive online portfolio selection

The class of defensive online portfolio selection algorithms,designed for fi nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game- Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasize the relevance of the proposed online investment algorithm which signi fi cantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.on-line portfolio selection; universal portfolio; defensive strategy