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. 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.
3. 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.
4. Strategic Broadcasting of a Championship: to Earn More from Ads or to Incentivize Subscription? (joint with Igor Karpov)
At the beginning of the Russian (Football) Premier League (RPL) 2018/19 season, many TV viewers have noticed that Russian sports free-to-air channel Match TV radically changed the broadcasting strategy. A significant drop in the percentage of broadcasts of best teams among all broadcasts was, most likely, associated with a launch of a new paid channel Match Premier which belongs to the same TV holding. Henceforth, Match Premier subscribers can watch all RPL matches live, while Match TV broadcasts only one match per matchday. The TV holding management faces the trade-off between inducing viewers to subscribe to the paid channel and getting revenues from advertisements on the popular free-to-air channel. It seems intuitive that for some markets, the corner solution of transferring all broadcasts to the paid channel is optimal. The same counts for the corner solution of broadcasting the top match per matchday on the free-to-air channel. However, the strategy of broadcasting a rather weak match on the free-to-air channel seems puzzling. We propose a theoretical model of broadcasting the championship and demonstrate that under some parameter values broadcasting a weak match free of charge is indeed the profit-maximizing strategy.
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. 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.
3. 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.
4. Strategic Broadcasting of a Championship: to Earn More from Ads or to Incentivize Subscription? (joint with Igor Karpov)
At the beginning of the Russian (Football) Premier League (RPL) 2018/19 season, many TV viewers have noticed that Russian sports free-to-air channel Match TV radically changed the broadcasting strategy. A significant drop in the percentage of broadcasts of best teams among all broadcasts was, most likely, associated with a launch of a new paid channel Match Premier which belongs to the same TV holding. Henceforth, Match Premier subscribers can watch all RPL matches live, while Match TV broadcasts only one match per matchday. The TV holding management faces the trade-off between inducing viewers to subscribe to the paid channel and getting revenues from advertisements on the popular free-to-air channel. It seems intuitive that for some markets, the corner solution of transferring all broadcasts to the paid channel is optimal. The same counts for the corner solution of broadcasting the top match per matchday on the free-to-air channel. However, the strategy of broadcasting a rather weak match on the free-to-air channel seems puzzling. We propose a theoretical model of broadcasting the championship and demonstrate that under some parameter values broadcasting a weak match free of charge is indeed the profit-maximizing strategy.
Economics, Game Theory, Computer Science, Sports Studies
Dmitry Dagaev
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