1. Strategizing with AI: Insights from a Beauty Contest Experiment (joint with Sofia Paklina and Petr Parshakov) (pdf)
A Keynesian beauty contest is a wide class of games of guessing the most popular strategy among other players. In particular, guessing a fraction of a mean of numbers chosen by all players is a classic behavioral experiment designed to test level-k reasoning patterns among various groups of people. The previous literature reveals that the sophistication level of opponents is an important factor affecting the outcome of the game. Smarter decision makers choose strategies that are closer to theoretical Nash equilibrium and demonstrate faster convergence to equilibrium in iterated contests with information revelation. In the level-k reasoning framework, the Nash equilibrium is played only by infinitely advanced players. We run a series of virtual experiments with an AI player, GPT-4, who plays against various groups of players. We test how advanced is this learning language model compared to human players by replicating some of the classic experiments. It is shown that GPT-4 takes into account the opponents' level of sophistication and adapts by changing the strategy. However, the transformation of the particular values of parameters to output data does not necessarily respect the comparative statics of the model. Lasso regression analysis revealed a closer alignment of AI-generated guesses to strategic thinking compared to human participants. Our results contribute to the discussion on the accuracy of modeling human economic agents by artificial intelligence.
2. Brinkmanship in Antagonistic Centipede: Evidence from a Natural Experiment (joint with Daniil Starikov and Gleb Vasiliev)
The centipede game serves as an illustration of a strategic interaction where players typically deviate from a subgame perfect Nash equilibrium. In previous laboratory experiments, the participants usually observe the tree of the centipede game, and the payoffs are given explicitly. Even in such rather simple conditions, the mental capacity is linked to following the equilibrium path (Palacios-Huerta and Volij, 2009). In this paper, we investigate the top athletes' behavior in a centipede-like game that is eventually played by Formula 1 drivers during each race. When two drivers are close to each other, they engage in a game where the goal is to be in front of the opponent. One of the dimensions of this game is related to the pit stop decision. On each lap, each driver, the leader and the pursuer, decide sequentially whether to go for a pit stop and change the tire. Using the intra-race dataset from several Formula 1 seasons, we estimate the effectiveness of two large classes of the pursuer's strategies: the undercuts (going for a pit stop earlier than the leader) and the overcuts (going for a pit stop later than the leader). It appears that the expected value of an undercut follows the inverted U-shape curve. Therefore, the pursuer has incentives to postpone the undercut decision until some optimal lap. At the same time, the leader can try to defend himself from an undercut and make the pit stop first. In this antagonistic centipede-like game, the players do not play equilibrium strategies.
3. Antagonistic sequential games with ties between players with limited search capacity
I consider an important class of antagonistic sequential games of value 0 with ties, where players do not have enough memory capacity to solve the game using backward induction. Checkers and supposedly chess belong to this class. In such games the level of human players is associated with the number and severity of mistakes (deviations from the subgame perfect equilibrium). One of the most popular ways to predict an outcome of such games is based on the paired comparison model. I show formally that for this class of games a predictive model that matches the empirical evidence, cannot be obtained in a paired comparison framework: two types of the desirable monotonicity lead to incompatibility. A relaxation of monotonicity properties that allows a solution to be found is also proposed in the paper.
4. Hosting Sports Mega-Events: The Costs of Ensuring Rotation (joint with Anastasia Nebolsina)
After the equivocal voting that determined the host country of the FIFA World Cup 2006, the International Federationa of Football Associations (FIFA) introduced rotation policy in order to provide an opportunity to host the major football tournament to the countries from different continents. When the goal was achieved, FIFA abolished the rotation rule. To investigate what factors could prevent the rotation to hold naturally in equilibrium as a result of competition we propose a multi-period game-theoretic model which simulates the interaction between the candidate countries and the Committee which grants the hosting rights. Solving the model for SPNE, we estimate the cost of artificial restrictions that ensure rotation. These results could be used for changing the decision-making process in FIFA and other similar organizations.
5. Strategic Broadcasting of a Championship: to Earn More from Ads or to Incentivize Subscription? (joint with Igor Karpov) (pdf)
Consider a company that owns two sports TV channels: a popular free-to-air channel and a narrow-profile pay one. The company bought the broadcasting rights for a round-robin championship. When developing the broadcasting strategy, the company's management faces the trade-off between inducing viewers to subscribe to the pay channel and getting revenues from advertisements on the free-to-air channel. Motivated by an anecdotal case of a significant drop in the percentage of broadcasts of best teams among all broadcasts on a free-to-air channel, we propose a theoretical model of broadcasting the championship. We demonstrate that a wide range of strategies can be optimal depending on the market parameters. Whereas the intermediate strategy of broadcasting just weak matches (instead of broadcasting top matches or broadcasting nothing) on the free-to-air channel seems puzzling, we show formally that it can be fully rational for some market configurations. Therefore, we rationalize the puzzling strategy used by the company's management in the motivational example.
A Keynesian beauty contest is a wide class of games of guessing the most popular strategy among other players. In particular, guessing a fraction of a mean of numbers chosen by all players is a classic behavioral experiment designed to test level-k reasoning patterns among various groups of people. The previous literature reveals that the sophistication level of opponents is an important factor affecting the outcome of the game. Smarter decision makers choose strategies that are closer to theoretical Nash equilibrium and demonstrate faster convergence to equilibrium in iterated contests with information revelation. In the level-k reasoning framework, the Nash equilibrium is played only by infinitely advanced players. We run a series of virtual experiments with an AI player, GPT-4, who plays against various groups of players. We test how advanced is this learning language model compared to human players by replicating some of the classic experiments. It is shown that GPT-4 takes into account the opponents' level of sophistication and adapts by changing the strategy. However, the transformation of the particular values of parameters to output data does not necessarily respect the comparative statics of the model. Lasso regression analysis revealed a closer alignment of AI-generated guesses to strategic thinking compared to human participants. Our results contribute to the discussion on the accuracy of modeling human economic agents by artificial intelligence.
2. Brinkmanship in Antagonistic Centipede: Evidence from a Natural Experiment (joint with Daniil Starikov and Gleb Vasiliev)
The centipede game serves as an illustration of a strategic interaction where players typically deviate from a subgame perfect Nash equilibrium. In previous laboratory experiments, the participants usually observe the tree of the centipede game, and the payoffs are given explicitly. Even in such rather simple conditions, the mental capacity is linked to following the equilibrium path (Palacios-Huerta and Volij, 2009). In this paper, we investigate the top athletes' behavior in a centipede-like game that is eventually played by Formula 1 drivers during each race. When two drivers are close to each other, they engage in a game where the goal is to be in front of the opponent. One of the dimensions of this game is related to the pit stop decision. On each lap, each driver, the leader and the pursuer, decide sequentially whether to go for a pit stop and change the tire. Using the intra-race dataset from several Formula 1 seasons, we estimate the effectiveness of two large classes of the pursuer's strategies: the undercuts (going for a pit stop earlier than the leader) and the overcuts (going for a pit stop later than the leader). It appears that the expected value of an undercut follows the inverted U-shape curve. Therefore, the pursuer has incentives to postpone the undercut decision until some optimal lap. At the same time, the leader can try to defend himself from an undercut and make the pit stop first. In this antagonistic centipede-like game, the players do not play equilibrium strategies.
3. Antagonistic sequential games with ties between players with limited search capacity
I consider an important class of antagonistic sequential games of value 0 with ties, where players do not have enough memory capacity to solve the game using backward induction. Checkers and supposedly chess belong to this class. In such games the level of human players is associated with the number and severity of mistakes (deviations from the subgame perfect equilibrium). One of the most popular ways to predict an outcome of such games is based on the paired comparison model. I show formally that for this class of games a predictive model that matches the empirical evidence, cannot be obtained in a paired comparison framework: two types of the desirable monotonicity lead to incompatibility. A relaxation of monotonicity properties that allows a solution to be found is also proposed in the paper.
4. Hosting Sports Mega-Events: The Costs of Ensuring Rotation (joint with Anastasia Nebolsina)
After the equivocal voting that determined the host country of the FIFA World Cup 2006, the International Federationa of Football Associations (FIFA) introduced rotation policy in order to provide an opportunity to host the major football tournament to the countries from different continents. When the goal was achieved, FIFA abolished the rotation rule. To investigate what factors could prevent the rotation to hold naturally in equilibrium as a result of competition we propose a multi-period game-theoretic model which simulates the interaction between the candidate countries and the Committee which grants the hosting rights. Solving the model for SPNE, we estimate the cost of artificial restrictions that ensure rotation. These results could be used for changing the decision-making process in FIFA and other similar organizations.
5. Strategic Broadcasting of a Championship: to Earn More from Ads or to Incentivize Subscription? (joint with Igor Karpov) (pdf)
Consider a company that owns two sports TV channels: a popular free-to-air channel and a narrow-profile pay one. The company bought the broadcasting rights for a round-robin championship. When developing the broadcasting strategy, the company's management faces the trade-off between inducing viewers to subscribe to the pay channel and getting revenues from advertisements on the free-to-air channel. Motivated by an anecdotal case of a significant drop in the percentage of broadcasts of best teams among all broadcasts on a free-to-air channel, we propose a theoretical model of broadcasting the championship. We demonstrate that a wide range of strategies can be optimal depending on the market parameters. Whereas the intermediate strategy of broadcasting just weak matches (instead of broadcasting top matches or broadcasting nothing) on the free-to-air channel seems puzzling, we show formally that it can be fully rational for some market configurations. Therefore, we rationalize the puzzling strategy used by the company's management in the motivational example.
Economics, Game Theory, Computer Science, Sports Studies
Dmitry Dagaev
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