Strategic Sophistication Research Articles

Where Power Resides: Evidence from the Chairman's Paradox

We investigate the effects of voting power in a committee in which one member (the chairman) holds, on top of a regular vote, also the power to break ties. In contrast to the equilibrium prediction under strategic voting, known as the Chairman’s Paradox, experimental data reveals that the tie-breaking power of the chairman is large and real. The chairman is able to induce her preferred outcome much more often than predicted, but only partially because of exercising tie-breaking power directly. The advantage of the chairman is largely determined by the limited strategic sophistication of committee members and the chairman’s salient position in the committee.

Adolescents, cognitive ability, and minimax play

We conduct experiments with adolescent participants on repeated fixed play in three different zero-sum games which have mixed strategy minimax solutions. Further, we collect subject information on cognitive abilities and participation rates in competitive activities. We find the adolescents’ correspondences with and deviations from minimax play largely consistent with previously and widely studied adult populations. Further, we find strategic sophistication in terms of implementation of the mixed minimax strategy as well as earnings are not correlated with cognitive ability or experience in competitive situations.

Gender Differences and Stereotypes in the Beauty Contest

Recent literature has emphasized that individuals display different depths of reasoning when playing games. In this paper, we explore gender differences in strategic sophistication and study whether these differences are endogenous. We report results from two different experiments employing the beauty contest. In the first, large study, we show that females react very strongly to incentives to the extent that gender differences disappear when a monetary prize is awarded. In the second study, we use a within subject design to analyze how depth of reasoning varies with gender priming and the gender composition of the set of players. We corroborate that females display higher levels of sophistication and even overtake males when incentives are provided and gender is primed. On the other hand, males who believe that females are better in the game display higher sophistication when playing against females.

On the Persistence of Strategic Sophistication

We examine whether the ‘Level-k’ model of strategic behavior generates reliable cross-game predictions within an individual. We find no correlation in subjects’ estimated levels of reasoning across two families of games. Furthermore, estimating a higher level for Ann than Bob in one family of games does not predict their ranking in the other. Direct tests of strategic reasoning generally do not predict estimated levels. Within families of games, we find that levels are fairly consistent within one family, but not the other. Our results suggest that the use of Level-k reasoning varies by game, making prediction difficult.

Decision time and steps of reasoning in a competitive market entry game

Entry decisions in market entry games usually depend on the belief about how many others are entering the market, the belief about the own rank in a real effort task, and subjects’ risk preferences. In this paper I am able to replicate these basic results and examine two further dimensions: (i) the level of strategic sophistication, which has a positive impact on entry decisions, and (ii) the impact of time pressure, which has a (partly) negative influence on entry rates. Furthermore, when ranks are determined using a real effort task, differences in entry rates are explainable by higher competitiveness of males. Additionally, I show that individual characteristics are more important for the entry decision in more competitive environments.

Strategic sophistication of individuals and teams. Experimental evidence

Many important decisions require strategic sophistication. We examine experimentally whether teams act more strategically than individuals. We let individuals and teams make choices in simple games, and also elicit first- and second-order beliefs. We find that teams play the Nash equilibrium strategy significantly more often, and their choices are more often a best response to stated first order beliefs. Distributional preferences make equilibrium play less likely. Using a mixture model, the estimated probability to play strategically is 62% for teams, but only 40% for individuals. A model of noisy introspection reveals that teams differ from individuals in higher order beliefs.

Cognitive ability and strategic sophistication

In three experiments we examine the extent to which strategic sophistication (i.e., inductive reasoning, iterative dominance and level-k thinking) is determined by broader cognitive skills. In the first experiment we replicate previous results showing strong associations between cognitive ability and sophistication in a game of iterative dominance and show that similar results arise in a game requiring induction. In the second two experiments we extend the literature in new directions. In Experiment 2 we modify the games to better capture participantsʼ ability to reason inductively and predict the sophistication of others and, again, find strong associations between cognitive ability, measured using a common IQ test, and sophistication. In Experiment 3 we examine more closely the causal nature of the relationship between cognitive ability and sophistication. We use a standard tool from cognitive psychology to randomly shock the cognitive ability of participants and show that this significantly affects game performance.

Cognitive Load and Strategic Sophistication

We study the relationship between the cognitive load manipulation and strategic sophistication. The cognitive load manipulation is designed to reduce the subject's cognitive resources that are available for deliberation on a choice. In our experiment, subjects are placed under a large cognitive load (given a difficult number to remember) or a low cognitive load (given a number which is not difficult to remember). Subsequently, the subjects play a one-shot game then they are asked to recall the number. This procedure is repeated for various games, where a new number is given for each game. We find a nuanced and nonmonotonic relationship between cognitive load and strategic sophistication. This relationship is consistent with two effects. First, subjects under a high cognitive load tend to exhibit behavior consistent with the reduced ability to compute the optimal decision. Second, the cognitive load tends to affect the subject's perception of their relative standing in the distribution of the available cognitive resources. The net result of these two effects depends on the strategic setting. Our experiment provides evidence on the literature which examines the relationship between measures of cognitive ability and strategic sophistication.

Information and beliefs in a repeated normal-form game

We study beliefs and actions in a repeated normal-form game. Using a level-k model of limited strategic reasoning and allowing for other-regarding preferences, we classify action and belief choices with regard to their strategic sophistication and study their development over time. In addition to a baseline treatment with common knowledge of the game structure, feedback about actions in the previous period and random matching, we run treatments (i) with fixed matching, (ii) without information about the other player’s payoffs, and (iii) without feedback about previous play. In all treatments with feedback, we observe more strategic play (increasing by 15 percent) and higher-level beliefs (increasing by 18 percent) over time. Without feedback, neither beliefs nor actions reach significantly higher levels of reasoning (with increases of 2 percentage points for actions and 6 percentage points for beliefs). The levels of reasoning reflected in actions and beliefs are highly consistent, but less so for types with lower levels of reasoning.

Democracy, populism, and (un)bounded rationality

In this paper we aim to understand how bounded rationality affects performance of democratic institutions. We consider policy choice in a representative democracy when voters do not fully anticipate a politician's strategic behavior to manipulate his reelection chances. We find that this limited strategic sophistication affects policy choice in a fundamental way. Under perfect sophistication, a politician does not make any use of his private information but completely panders to voters' opinions. In contrast, under limited sophistication, a politician makes some use of private information and panders only partially. Limited sophistication crucially determines how welfare under representative democracy compares to welfare under alternative political institutions such as direct democracy or governance by experts. We find that, under limited strategic sophistication, representative democracy is preferable to the other institutions from an ex ante perspective.

Are Self-Regarding Subjects More Rational?

To investigate the relationship between the depth of strategic thinking and social preferences we ask subjects in an experiment to perform dictator games and a guessing game. The guessing game measures depth of strategic thinking while dictator games control for social preferences. When performing a comparison within the same degree of strategic reasoning, self-regarding subjects show more strategic sophistication than other subjects.

Information and Beliefs in a Repeated Normal-Form Game

We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure, feedback about choices in the previous period and random matching, we run treatments (i) with fixed matching, (ii) without information about the opponent’s payoffs, and (iii) without feedback about previous play. Using Stahl and Wilson’s (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. In the treatments with feedback and full information about the game, we observe more strategic play, more best-responses to beliefs and more accurate beliefs over time. While feedback is the main driving force of learning to play strategically and for forming beliefs that accurately predict the behavior of the opponent, both incomplete information about the opponent’s payoffs or lack of feedback lead to a stagnation of best-response rates over time.

Strategic Sophistication of Adolescents: Evidence from Experimental Normal-Form Games

We examine the strategic sophistication of adolescents, aged 10 to 17 years, in experimental normal-form games. Besides making choices, subjects have to state their first- and secondorder beliefs. We find that choices are more often a best reply to beliefs if any player has a dominant strategy and equilibrium payoffs are not too unequal. Using a mixture model we can estimate for each subject the probability to be any of eight different strategic and nonstrategic types. The econometric estimation reveals that older subjects are more likely to eliminate dominated strategies, and that subjects with good math grades are more strategic.

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

In this paper, we test the effect of on initial strategic behavior in normal form games, where the term descriptive indicates all those features which can be modified without altering the (Nash) equilibrium structure of a game. Our experimental subjects behaved according to some simple heuristics based on features, and we observed that these heuristics were stable even across strategically different games. These findings indicate the need to incorporate features into models describing strategic sophistication in normal form games. Analysis of choice patterns and individual behavior indicates that non-equilibrium choices may derive from incorrect and simplified mental representations of the game structure, rather than from beliefs in other players' irrationality. We suggest how level-k and cognitive hierarchy models might be extended to account for heuristic-based and feature-based behavior.

Strategic Sophistication of Individuals and Teams in Experimental Normal-Form Games

Strategic Sophistication of Individuals and Teams in Experimental Normal-Form Games

Democracy, Populism, and (Un)bounded Rationality

In many instances, both voters and politicians are imperfectly informed about which policies are optimal. We analyze politicians’ policy choice in such situations. A distinctive element of our analysis is that we investigate how the strategic sophistication of voters’ beliefs about politicians’ behavior affects policy choice. This provides a novel approach in political economy that leads to a number of important insights. We show that these beliefs determine the strength of self-serving politicians’ incentives to engage in populism. Surprisingly, limited strategic sophistication of voters weakens politicians’ incentives to pander to public opinion. The reason is that politicians know that such voters expect them to choose a policy that is not perfectly pandering to public opinion. Furthermore, when comparing the welfare ranking of different constitutional regimes, we find that limited strategic sophistication of voters makes indirect democracy relatively more attractive compared to the case of full strategic rationality – and often more attractive than alternative constitutional regimes.

Democracy, Populism, and (Un)bounded Rationality

In this paper we aim to understand how bounded rationality affects performance of democratic institutions. We consider policy choice in a representative democracy when voters do not fully anticipate a politician’s strategic behavior to manipulate his reelection chances. We find that this limited strategic sophistication affects policy choice in a fundamental way. Under perfect sophistication, a politician does not make any use of his private information but completely panders to voters’ opinions. In contrast, under limited sophistication, a politician makes some use of private information and panders only partially. Limited sophistication crucially determines how welfare under representative democracy compares to welfare under alternative political institutions such as direct democracy or governance by experts. We find that, under limited strategic sophistication, representative democracy is preferable to the other institutions from an ex ante perspective.

What Do Australian Businesses Really Think of the ACCC, and Does it Matter?

The Australian Competition and Consumer Commission ('ACCC') has been heavily criticised by business. This paper reports systematic, representative quantitative evidence on how large Australian businesses perceive the ACCC as a regulator in order to understand how these opinions are likely to affect compliance with trade practices regulation. First, we briefly review competing theories about what motivates businesses to comply or not comply with the law, and why their opinions of regulators matter for compliance. Second, we report survey results on business opinions of the ACCC along six dimensions that are explained in the paper - the ACCC's procedural and substantive justice, the likelihood and severity of ACCC enforcement action, the ACCC's strategic sophistication, how undogmatic it is, how accommodating it is, and whether it is biased in the way it targets large and small businesses for enforcement action. Third, we examine the extent to which our survey respondents' reported opinions of the ACCC are based on actual experience or not, and to what extent they are in line with their opinions of the other main national business regulators in Australia. Finally, we test the relationship between businesses' opinions of the ACCC and their attitudes towards trade practices compliance. We find that business opinions of the ACCC as reported in our survey are mostly not as negative as media reports might have suggested, and that opinions of the ACCC do relate to attitudes towards compliance, but not always in the ways that previous theory and research might suggest.

Analysts, Incentives, and Exaggeration

Sell-side analysts are compensated, at least in part, by brokerage commissions. These commissions create an incentive to bias forecasts to generate trade. Thus, analysts have clear economic incentives to deceive and traders have economic incentives to detect deception. Prior analytical theories of information transmission games starkly predict that there will always be some deception (with trade) at best and uninformative messages (and no trade) at worst when the sender's and receiver's incentives are not aligned. Prior experimental evidence of information transmission games show senders do elect to deceive, although they send messages more informative than theory predicts. Likewise, receivers rely more upon messages than theory predicts. Can behavior that deviates from prediction be explained by normative social behavior, such as trust and honesty? Alternatively, are subjects boundedly rational, failing to sufficiently consider other players' incentives when predicting their decisions? To answer these questions, I design and conduct an experiment to investigate whether forecasting and trading behaviors are best explained by analytical theory, limited strategic sophistication, or social norms. The experimental results confirm a majority of subjects adopt dishonest forecasting strategies, but at the same time, a majority of subjects adopts trusting trading strategies. Additionally, subjects do not appear to revise trading behavior despite evidence of deceptive forecasts. The results suggest subjects' behavior within the setting is better explained by limited strategic sophistication than by social normative behavior or sequential rationality.

RATIONALIZATION IN SIGNALING GAMES: THEORY AND APPLICATIONS

Focusing on signaling games, I illustrate the relevance of the rationalizability approach for the analysis multistage games with incomplete information. I define a class of iterative solution procedures, featuring a notion of "forward induction": the Receiver tries to explain the Sender's message in a way which is consistent with the Sender's strategic sophistication and certain given restrictions on beliefs. The approach is applied to some numerical examples and economic models. In a standard model with verifiable messages a full disclosure result is obtained. In a model of job market signaling the best separating equilibrium emerges as the unique rationalizable outcome only when the high and low types are sufficiently different. Otherwise, rationalizability only puts bounds on the education choices of different types.