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on Sports and Economics |
| By: | Christian Turk; Nicholas Polson; Shiva Maharaj |
| Abstract: | Gambits are central to human decision making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study Gambits and behavioral economics. Our theory is based on the Bellman optimality path for sequential decision making. This allows us to calculate the Q values of a Gambit where material (usually a pawn) is sacrificed for dynamic play. On the empirical side, we study the effectiveness of a number of popular chess Gambits. This is a natural setting as chess Gambits require a sequential assessment of a set of moves (a.k.a. policy) after the Gambit has been accepted. Our analysis uses Stockfish 14 to calculate the optimal Bellman Q values. To test whether Bellman's equation holds in play, we estimate the transition probabilities to the next board state via a database of expert human play. This then allows us to test whether the Gambiteer is following the optimal path in his decision making. Our methodology is applied to the popular Stafford, Reverse Stafford (a.k.a. Boden-Kieretsky-Morphy), Smith-Morra, Goring, Danish, and Halloween Gambits. We conclude with directions for future research. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.02755&r= |
| By: | Steven DiSilvio (Anna); Yu (Anna); Luo; Anthony Ozerov |
| Abstract: | Figgie is a card game that approximates open-outcry commodities trading. We design strategies for Figgie and study their performance and the resulting market behavior. To do this, we develop a flexible agent-based discrete-event market simulation in which agents operating under our strategies can play Figgie. Our simulation builds upon previous work by simulating latencies between agents and the market in a novel and efficient way. The fundamentalist strategy we develop takes advantage of Figgie's unique notion of asset value, and is, on average, the profit-maximizing strategy in all combinations of agent strategies tested. We develop a strategy, the "bottom-feeder", which estimates value by observing orders sent by other agents, and find that it limits the success of fundamentalists. We also find that chartist strategies implemented, including one from the literature, fail by going into feedback loops in the small Figgie market. We further develop a bootstrap method for statistically comparing strategies in a zero-sum game. Our results demonstrate the wide-ranging applicability of agent-based discrete-event simulations in studying markets. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.00879&r= |
| By: | José De Sousa (Université Paris-Saclay); Guillaume Hollard (Institut Polytechnique de Paris (IP Paris)) |
| Abstract: | Women are under-represented in top positions, such as Business, Politics and Science. The same under-representation occurs in chess, providing us with a unique opportunity to analyze this phenomenon. We find a macro gender gap in every country: there are fewer female than male players, especially at the top, and women have lower average rankings. One contribution of this paper is to link the macro gender gap to micro gender differences. Comparing millions of individual games, we find that women’s scores are about 2% lower than expected when playing a man rather than a woman with identical rating, age and country. Using a simple theoretical model, we explain how a small micro gap may affect women’s long-run capital formation. A small difference in outcomes generates a small difference in effort, and thus a lower future ranking. By reducing effort and increasing the probability of quitting, both effects accumulate to discourage women from competing for top positions. |
| Keywords: | macro gender gap; micro gender differences; under-representation |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/5msrbb0rie9sjq3c4ejgb2v91o&r= |