Information encryption in the expert management of strategic uncertainty

Strategic agents in incomplete-information environments have a conflicted relationship with uncertainty: it can keep them unpredictable to their opponents, but it must also be overcome to predict the actions of those opponents. We use a multivariate generalization of information theory to characterize the information processing behavior of strategic reasoning experts. We compare expert and novice poker players — "sharks" and "fish" — over 1.75 million hands of online two-player No-Limit Texas Hold’em (NLHE). Comparing the effects of privately known and publicly signaled information on wagering behavior, we find that the behavior of sharks coheres with information that emerges only from the interaction of public and private sources — “synergistic” information that does not exist in either source alone. This implies that the effect of public information on shark behavior is better encrypted: it cannot be reconstructed without access to the hidden state of private cards. Integrative information processing affects not only one’s own strategic behavior, but the ability of others to predict it. By characterizing the informational structure of complex strategic interactions, we offer a detailed account of how experts extract, process, and conceal valuable information in high-uncertainty, high-stakes competitive environments. Information encryption among poker sharks When valuable information is common knowledge, utility-maximizing strategic agents face a difficult problem. Failing to use the information means forgoing an opportunity to exploit opponents, but using it can make one more predictable to opponents. How do expert strategic reasoners manage the competing demands of maximizing utility and minimizing predictability? In games of incomplete information, is the choice between these goals inherently a tradeoff, or is it possible to have one without losing the other? Game experts are an excellent source of insight into how humans process strategic information in competitive settings. Interest in strategic experts, and chess experts in particular, goes back to the very roots of both cognitive science and artificial intelligence (Chase & Simon, 1973). More recently, chess experts have attracted the attention of behavioral economists (Bühren & Frank, 2012; Gerdes, Gränsmark, & Rosholm, 2011; Levitt, List, & Sadoff, 2011), who have found, for example, that grandmasters exhibit impressively many levels of recursive strategic reasoning when playing simple economic games against each other, and that they adapt to novices by exhibiting fewer levels of recursive reasoning (Palacios-Huerta & Volij, 2009). Though the complete-information game of chess has received the most attention, theorists have been making progress on incomplete-information games since the 1950's, with a special focus on subgames of poker (Billings, Davidson, Schaeffer, & Szafron, 2002; Kuhn, 1950). In a recent major advance, Bowling et al. present a type of solution to two-player limit Hold’em (Bowling, Burch, Johanson, & Tammelin, 2015; Sandholm, 2015). Subgames of poker have also proven useful for the experimental study of human strategic behavior (Laakasuo, Palomäki, & Salmela, 2014; Meyer, Meduna, Brosowski, & Hayer, 2013; Rapoport, Erev, Abraham, & Olson, 1997; Seale & Phelan, 2009). As econometric methods are brought to bear in field settings, Information encryption among poker sharks