Stated belief and play in normal form games

Using data on one-shot games, we investigate the assumption that players respond to underlying expectations about their opponent�s behavior. In our laboratory experiments, subjects play a set of 14 two-person 3x3 games, and state first order beliefs about their opponent�s behavior. The sets of responses in the two tasks are largely inconsistent. Rather, we find evidence that the subjects perceive the games differently when they (i) choose actions, and (ii) state beliefs � they appear to pay more attention to the opponent�s incentives when they state beliefs than when they play the games. On average, they fail to best respond to their own stated beliefs in almost half of the games. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we can control for noise, and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant

Stated Beliefs and Play in Normal-Form Games

Using data on one-shot games, we investigate the assumption that players respond to underlying expectations about their opponent's behavior. In our laboratory experiments, subjects play a set of 14 two-person 3x3 games, and state first order beliefs about their opponent'sbehavior. The sets of responses in the two tasks are largely inconsistent. Rather, we findevidence that the subjects perceive the games differently when they (i) choose actions, and (ii) state beliefs _ they appear to pay more attention to the opponent's incentives when they state beliefs than when they play the games. On average, they fail to best respond to their own stated beliefs in almost half of the games. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we can control for noise, and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant.

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 and feedback about choices in the previous period, we run treatments (i) without feedback about previous play, (ii) with no information about the opponent’s payoffs and (iii) with random matching. 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. We use belief statements to check for the consistency of subjects’ actions with the stated beliefs as well as for the accuracy of their beliefs (relative to the opponent’s true choice). In the baseline treatment we observe more sophisticated play as well as more accurate beliefs and more best responses to beliefs over time. We isolate feedback as the main driving force of learning to play strategically and to form beliefs that accurately predict the behavior of the opponent.beliefs, experiments, strategic uncertainty, learning

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. ZUSAMMENFASSUNG - (Information und Erwartungen in einem wiederholten Normalformspiel) Wir untersuchen die Entwicklung von den Erwartungen über das Verhalten des anderen Spielers und den Entscheidungen in einem wiederholten Normalformspiel. Zusätzlich zum Haupttreatment mit common knowledge über das Spiel, Feedback über das Ergebnis in der vorigen Runde und zufälliger Zuordnung der Spieler, gibt es Kontrolltreatments mit (i) festen paarweisen Zuordnungen der Spieler, (ii) ohne Information über die Auszahlungen des anderen Spielers und (iii) ohne Feedback über das Ergebnis der vorigen Runde. Mit Hilfe von Stahl und Wilsons (1995) Modell begrenzten strategischen Verhaltens klassifizieren wir das Verhalten der Teilnehmer im Hinblick auf die strategische Sophistikation. In den Treatments mit Feedback und vollständiger Information über das Spiel nehmen strategisches Verhalten, beste Antworten auf die eigenen Erwartungen und die Akkuratheit der Erwartungen über die Zeit zu. Während Feedback der Hauptgrund dafür ist, dass die Teilnehmer lernen, sich strategisch zu verhalten und korrekte Erwartungen über das Verhalten des anderen Spielers zu bilden, führen sowohl unvollständige Information über die Auszahlungen des Gegenspielers als auch fehlendes Feedback zu einer Stagnation der Rate der besten Antworten über die Zeit.

Equilibrium Play and Best Response to (Stated) Beliefs in Constant Sum Games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our ex- periment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.Experiments, Constant Sum Games, Stated Beliefs

Equilibrium Play and Best Reply to (Stated) Beliefs in Constant Sum Games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence the way subjects play in simple but non trivial games and explain differences with previous work.Experiments Constant Sum Games Stated Beliefs

Best Responding to What? A Behavioral Approach to One Shot Play in 2x2 Games

We introduce a simple procedure to be used for selecting the strategies most likely to be played by inexperienced agents who interact in one shot 2x2 games. We start with an axiomatic description of a function that may capture players' beliefs. Various proposals connected with the concept of mixed strategy Nash equilibrium do not match this description. On the other hand minimax regret obeys all the axioms. Therefore we use minimax regret to approximate players' beliefs and we let players best respond to these conjectured beliefs. When compared with existing experimental evidences about one shot matching pennies games, this procedure correctly indicates the choices of the vast majority of the players. Applications to other classes of games are also explored

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 second-order 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 non-strategic 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.strategic thinking, beliefs, experiment, age, adolescents