Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study

Games 2013, 4, 776-794; doi:10.3390/g4040776 OPEN ACCESS games ISSN 2073-4336 www.mdpi.com/journal/games Article Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study Sibilla Di Guida 1,* and Giovanna Devetag 2 1 2 Solvay Brussels School of Economics and Management, European Center for Advanced Research in Economics and Statistics, Université Libre de Bruxelles, Avenue Roosevelt 50 CP 114, Bruxelles 1050, Belgium; E-Mail: Luiss Guido Carli, Department of Business and Management, Viale Pola 12, Roma 00198, Italy; E-Mail: * Author to whom correspondence should be addressed; E-Mail: ; Tel.: +32-2-650-5950; Fax: +32-2-650-4475. Received: 16 September 2013; in revised form: 5 December 2013 / Accepted: 12 December 2013 / Published: 18 December 2013 Abstract: In this paper, we claim that agents confronting with new interactive situations apply behavioral heuristics that drastically reduce the problem complexity either by neglecting the other players’ incentives, or by restricting attention to subsets of “salient” outcomes. We postulate that these heuristics are sensitive to the manipulation of those features that can be modified without altering the (Nash) equilibrium structure of the game. We call these features “descriptive”. We test experimentally the effect of these descriptive features on both choice behavior and cross-game similarity perception. Analysis of individual choices confirms our hypotheses, and suggests that non-equilibrium choices may derive from simplified mental models of the game structure, rather than from heterogeneous beliefs or limited iterative thinking. In addition, subjects tend to behave similarly in games sharing similar descriptive features, regardless of their strategic structure. Keywords: cross-game similarity; categorization; focal point; behavioral heuristic; individual behavior; one-shot game; response time Games 2013, 4 777 1. Introduction Every day, people face several decisions; most of them have risible consequences and can be dealt with almost automatically, only a few are crucial. Many of these decisions, however, are new, i.e., they have never been encountered before. The situations people face in their daily routine are in fact often similar to other situations previously encountered, but rarely identical. Then, how do people react to a strategic situation they have never encountered before? When do people perceive two situations as being similar? Behavioral game theory in the last decade has produced abundant experimental evidence in response to these questions, which in turn has informed empirically grounded modeling efforts. The enterprise has led to the development of new equilibrium concepts (e.g., Quantal Response Equilibrium [1], Cursed Equilibrium [2], to name a few) and of models that take on board individuals’ limited reasoning abilities (i.e., the vast family of the level-k models [3–5]). Behavioral models of game playing, although relaxing the most implausible assumptions of standard game theory, still rely on the notion of strategic thinking, i.e., they assume that players form beliefs about other players (in other words, players have a mental model of the other player’s strategic behavior) and try to maximize their utility given these beliefs (an exception is given by level-0 players in level-k models, who are assumed to choose a strategy randomly). Some of the available evidence, however, suggests a partly different picture of behavior in one-shot games, by pointing out that choice and belief might not be one the result of the other [6], by suggesting, more radically, that players may significantly underestimate their opponents' rationality [7], and finally, by hinting at the possibility that players may even act on the basis of a very simplified and/or incorrect model of the “true” strategic situation [8,9]. In this paper, we submit that players in several occasions may apply choice heuristics that imply a drastic simplification of the original decision problem, obtained either by ignoring the other players’ motivations or by ignoring a subset of the game outcomes. These heuristics have the property of being “vulnerable” to the influence of features other than those pertaining to the game inner strategic structure: as a consequence, predictable changes in observed behavior can occur as a function of the presence vs. absence of these features. More specifically, we argue that players in reasonably complex one-shot games, with no opportunity for learning and no feedback, at first look for “obvious” and “intuitive” solutions to the strategic problem they face: one such natural solution is picking a strategy which is both attractive and relatively safe, i.e., one with high payoff sum and low payoff variance. Alternatively, an equally “natural” solution is selecting the strategy supporting an outcome that is attractive for both players, which we call a focal point. The first heuristic is compatible with level-1 types in level-k models of strategic thinking [3–5] and may derive either from diffuse priors on the opponent’s play or from a tendency to ignore opponents’ moves entirely [7]. However, unlike in the models mentioned above, we assume that payoff variance (taken as an intuitive measure of the risk involved in choosing a strategy) plays an important role in determining level-1 behaviors. Although previous studies have investigated risk aversion in different economic settings [10–13], to the best of our knowledge, we are the first to test the role of payoff variance in influencing gaming behavior. The second heuristic is more strategic as it relies on Schelling salience [14–16] which has been identified in many previous experiments on Games 2013, 4 778 matching games and which is well known for its effectiveness in promoting coordination. However, we assume that the effect of salience is much more widespread than commonly thought, even promoting the choice of focal points that are not equilibrium outcomes, as is the case in our games. Only in the absence of features suggesting attractive and intuitive solutions may players start to reason more strategically in a standard game-theoretic sense, and even find their way to equilibrium. We also hypothesize that games sharing features such as the presence of a safe-and-attractive strategy and a focal point may trigger similar behaviors (at both the aggregate and individual levels), despite very different inner strategic structures; conversely, games which differ feature-wise but which present the same equilibrium properties may trigger very different behaviors. While similarity perception has been largely investigated in psychology [17,18], it was mostly neglected in economics (exceptions are [19–21]). We claim that theories of cross-game similarity are crucial when modeling important phenomena such as cross-game transfer and generalization. It is widely acknowledged that the games we play in real life are at most simila (...truncated)