Rational reasoning or adaptive behavior? Evidence from two-person beauty contest games

Many experiments have shown that human subjects do not necessarily behave in line with game theoretic assumptions and solution concepts. The reasons for this non-conformity are multiple. In this paper we study the argument whether a deviation from game theory is because subjects are rational, but doubt that others are rational as well, compared to the argument that subjects, in general, are boundedly rational themselves. To distinguish these two hypotheses, we study behavior in repeated 2-person and many-person Beauty- Contest-Games which are strategically different from one another. We analyze four different treatments and observe that convergence toward equilibrium is driven by learning through the information about the other player’s choice and adaptation rather than self-initiated rational reasoning.Beauty contest, Guessing game, Bounded rationality, Weak dominance, Learning

Gender differences in equilibrium play and strategic sophistication variability

We investigate the existence of gender differences in strategic sophistication in two weakly dominance solvable games where a prize is at stake. The first one is the two-person beauty contest, where strategies are numbers and players must perform mathematical operations. The second is the novel “gaze coach game”, where strategies are photographs of the eye region and the two players must assign emotional states to these images. We observe that females follow equilibrium play less often in the former game but not in the latter. Males display greater strategic sophistication variability. As a result, females are underrepresented among top performers in both games.</p

Progress in Behavioral Game Theory

Is game theory meant to describe actual choices by people and institutions or not? It is remarkable how much game theory has been done while largely ignoring this question. The seminal book by von Neumann and Morgenstern, The Theory of Games and Economic Behavior, was clearly about how rational players would play against others they knew were rational. In more recent work, game theorists are not always explicit about what they aim to describe or advise. At one extreme, highly mathematical analyses have proposed rationality requirements that people and firms are probably not smart enough to satisfy in everyday decisions. At the other extreme, adaptive and evolutionary approaches use very simple models-mostly developed to describe nonhuman animals-in which players may not realize they are playing a game at all. When game theory does aim to describe behavior, it often proceeds with a disturbingly low ratio of careful observation to theorizing

A cognitive hierarchy model of games

Players in a game are “in equilibrium” if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k − 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games

Iterated dominance and iterated best response in experimental "p-beauty contests"

Picture a thin country 1000 miles long, running north and south, like Chile. Several natural attractions are located at the northern tip of the country. Suppose each of n resort developers plans to locate a resort somewhere on the country's coast (and all spots are equally attractive). After all the resort locations are chosen, an airport will be built to serve tourists, at the average of all the locations including the natural attractions. Suppose most tourists visit all the resorts equally often, except for lazy tourists who visit only the resort closest to the airport; so the developer who locates closest to the airport gets a fixed bonus of extra visitors. Where should the developer locate to be nearest to the airport? The surprising game-theoretic answer is that all the developers should locate exactly where the natural attractions are. This answer requires at least one natural attraction at the northern tip, but does not depend on the fraction of lazy tourists or the number of developers (as long as there is more than one)

Taxi Drivers and Beauty Contests

The trading floor of the New York Stock Exchange. The British economist John Maynard Keynes likened playing the market to voting for the prettiest face in a beauty contest; hence the second part of this article’s title

One, two, (three), infinity: Newspaper and lab beauty-contest experiments

"Beauty-contest" is a game in which participants have to choose, typically, a number in [0,100], the winner being the person whose number is closest to a proportion of the average of all chosen numbers. We describe and analyze Beauty-contest experiments run in newspapers in UK, Spain, and Germany and find stable patterns of behavior across them, despite the uncontrollability of these experiments. These results are then compared with lab experiments involving undergraduates and game theorists as subjects, in what must be one of the largest empirical corroborations of interactive behavior ever tried. We claim that all observed behavior, across a wide variety of treatments and subject pools, can be interpreted as iterative reasoning. Level-1 reasoning, Level-2 reasoning and Level-3 reasoning are commonly observed in all the samples, while the equilibrium choice (Level-Maximum reasoning) is only prominently chosen by newspaper readers and theorists. The results show the empirical power of experiments run with large subject-pools, and open the door for more experimental work performed on the rich platform offered by newspapers and magazines.Experiments, bounded rationality, Beauty-contest, parallelism, Leex

Billiards and Brains: Cognitive Ability and Behavior in a p-Beauty Contest

"Beauty contests" are well-studied, dominance-solvable games that generate two interesting results. First, most behavior does not conform to the unique Nash equilibrium. Second, there is considerable unexplained heterogeneity in behavior. In this work, we evaluate the relationship between beauty contest behavior and cognitive ability. We find that subjects with high cognitive ability exhibit behavior that is closer to the Nash equlibrium. We examine this finding through the prism of economic and biological theory.beauty contest; rationality; cognitive ability; Nash equlibrium

The neural basis of bounded rational behavior

Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting – the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. We apply a cognitive hierarchy model to classify subject’s choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. We found a correlation between levels of strategic reasoning and activity in a neural network related to mentalizing, i.e. the ability to think about other’s thoughts and mental states. Moreover, brain data showed how complex cognitive processes subserve the higher level of reasoning about others. We describe how a cognitive hierarchy model fits both behavioural and brain data.Game theory, Bounded rationality, Neuroeconomics