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Game theory: the story on HearLore | HearLore
— Ch. 1 · Foundations And Early History —
Game theory.
~8 min read · Ch. 1 of 7
In 1564, Gerolamo Cardano wrote Liber de ludo aleae, a manuscript on games of chance that remained unpublished until 1663. This early work laid the groundwork for mathematical probability studies involving gambling and strategic decision-making. Pierre-Simon Laplace later expanded these ideas in the 18th century, though his contributions were not fully recognized at the time. The field gained momentum when Blaise Pascal and Pierre de Fermat exchanged letters in 1654 about dividing stakes in interrupted games of chance. Christiaan Huygens published De ratiociniis in ludo aleæ in 1657, introducing the concept of expectation to reasoning about game structures. Charles Waldegrave sent a letter in 1713 analyzing le her, a two-person card game, providing what is now called the minimax mixed strategy solution. Antoine Augustin Cournot presented a model of competition in oligopolies in 1838 through Researches into the Mathematical Principles of the Theory of Wealth. Joseph Bertrand critiqued Cournot's approach in 1883 with an alternative price competition model formalized by Francis Ysidro Edgeworth. Ernst Zermelo proved in 1913 that optimal chess strategy is strictly determined using set theory applications. John von Neumann established game theory as an independent field with his 1928 paper On the Theory of Games of Strategy. His proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, becoming standard method in mathematical economics. Von Neumann co-authored Theory of Games and Economic Behavior with Oskar Morgenstern in 1944, which included cooperative game analysis for multiple players.
Nash Equilibrium And Modern Theory
John Nash developed a criterion for mutual consistency of player strategies known as the Nash equilibrium in 1950. This concept applied to wider varieties of games than previous criteria proposed by von Neumann and Morgenstern. Nash proved every finite n-player non-zero-sum non-cooperative game has what is now called a Nash equilibrium in mixed strategies. Game theory experienced significant activity during the 1950s when concepts like the core, extensive form game, fictitious play, repeated games, and Shapley value were developed. Merrill M. Flood and Melvin Dresher conducted experiments at RAND Corporation involving the prisoner's dilemma as part of global nuclear strategy investigations. Reinhard Selten introduced subgame perfect equilibria in 1965, refining the Nash equilibrium further. He later added trembling hand perfection to this framework. The 1970s saw extensive application of game theory to biology through John Maynard Smith's work on evolutionarily stable strategies. Concepts including correlated equilibrium, trembling hand perfection, and common knowledge were introduced and analyzed during this period. Thomas Schelling worked on dynamic models and early examples of evolutionary game theory in the 2000s. Robert Aumann contributed to equilibrium school by introducing equilibrium coarsening and correlated equilibria while developing formal analysis of common knowledge assumptions.
When did Gerolamo Cardano write Liber de ludo aleae?
Gerolamo Cardano wrote Liber de ludo aleae in 1564. The manuscript remained unpublished until 1663.
Who established game theory as an independent field and when?
John von Neumann established game theory as an independent field with his 1928 paper On the Theory of Games of Strategy. He later co-authored Theory of Games and Economic Behavior with Oskar Morgenstern in 1944.
What is the Nash equilibrium and who developed it?
John Nash developed a criterion for mutual consistency of player strategies known as the Nash equilibrium in 1950. Nash proved every finite n-player non-zero-sum non-cooperative game has what is now called a Nash equilibrium in mixed strategies.
How does evolutionary game theory explain animal behavior?
Game theory explained approximately 1:1 sex ratios as result of evolutionary forces acting on individuals trying to maximize grandchildren numbers. Biologists used evolutionary game theory to explain emergence of animal communication through signaling games and other communication frameworks.
When did John Maynard Smith receive the Crafoord Prize?
John Maynard Smith received the Crafoord Prize for applying evolutionary game theory in 1999. This award recognized contributions to biological applications of the field.
Antoine Augustin Cournot applied game-theoretic analysis to economics in 1838 with his solution of the Cournot duopoly model. Modern applications include auctions, bargaining, mergers and acquisitions pricing, fair division, duopolies, oligopolies, social network formation, agent-based computational economics, general equilibrium, mechanism design, and voting systems. Vincent P. Crawford published Theory and Experiment in the Analysis of Strategic Interaction in 1997 covering experimental economics and behavioral economics. Faruk Gul wrote about behavioural economics and game theory in papers spanning 1986 to 2003 for Princeton University Press. Martin Shubik authored Game Theory Models and Methods in Political Economy in 1981 and A Game-Theoretic Approach to Political Economy in 1987 through MIT Press. The Chartered Institute of Procurement & Supply conducted surveys showing game theory application to procurement activity reached 19% across respondents in their third annual survey from 2019. Sixty-five percent of participants predicted future growth in game theory applications while 70% reported only basic or below basic understanding of the field. Twenty percent had undertaken on-the-job training in game theory and 50% said new software solutions were desirable. Ninety percent stated they lacked necessary software for their work. Project management scenarios involving investors, contractors, subcontractors, governments, and customers use two-player games predominantly to model decision-making processes. Five distinct types of games appear in project management including government-sector-private-sector games, contractor-contractor games, contractor-subcontractor games, subcontractor-subcontractor games, and games involving other players.
Evolutionary Biology And Animal Behavior
Ronald Fisher began using game-theoretic analysis in biology during the 1930s to study animal behavior before the term existed. John Maynard Smith published Evolution and the Theory of Games in 1982 applying evolutionary game theory to biological phenomena. The evolutionarily stable strategy concept first introduced by Maynard Smith became best-known equilibrium in biology despite initial motivation not involving mental requirements of Nash equilibrium. Every evolutionarily stable strategy is a Nash equilibrium though its development did not require rationality assumptions. Game theory explained approximately 1:1 sex ratios as result of evolutionary forces acting on individuals trying to maximize grandchildren numbers. Biologists used evolutionary game theory to explain emergence of animal communication through signaling games and other communication frameworks. Mobbing behavior where prey animals attack larger predators represents spontaneous emergent organization among many species. Ants exhibit feed-forward behavior akin to fashion according to Paul Ormerod's Butterfly Economics research. The game of chicken analyzed fighting behavior and territoriality in preface to Evolution and the Theory of Games. Biological altruism describes situations where organisms act benefiting others while being detrimental to themselves without conscious intent. Vampire bats regurgitate blood obtained from hunting nights to give group members who failed to feed. Worker bees care for queen bee entire lives without mating while vervet monkeys warn group members of predator approaches even when endangering individual survival chances. Hamilton's rule explains evolutionary rationale behind selection with equation C < B × R showing cost must be less than benefit multiplied by coefficient of relatedness.
Computer Science And Artificial Intelligence
Game theory plays increasingly important role in logic and computer science with several logical theories having basis in game semantics. Computer scientists use games to model interactive computations providing theoretical basis to multi-agent systems field. Yao's principle serves as game-theoretic technique proving lower bounds on computational complexity of randomized algorithms especially online algorithms. Internet development motivated algorithm creation for finding equilibria in games, markets, computational auctions, peer-to-peer systems, security and information markets. Algorithmic game theory combines computational algorithm design and analysis of complex systems with economic theory through mechanism design frameworks. Game theory applications in artificial intelligence include developing autonomous systems making complex decisions in uncertain environments. Multi-agent system formation, reinforcement learning, and mechanism design represent key areas within AI machine learning context. By modeling behavior of other agents and anticipating actions, AI systems make better decisions operating more effectively. Research addresses perfect and imperfect information games with very complex combinatorial structures like chess, Go, or backgammon where no provable optimal strategies found yet. Practical solutions involve computational heuristics including alpha-beta pruning or artificial neural networks trained by reinforcement learning making games tractable in computing practice. Partially observable stochastic game represents gold standard though few realistic problems computationally feasible in this representation.
Political Science And Defense Strategy
Anthony Downs applied Hotelling firm location model to political process in 1957 book An Economic Theory of Democracy showing candidates converge to ideology preferred by median voter if voters fully informed. Game theory applied in 1962 to Cuban Missile Crisis during John F. Kennedy presidency explaining stability forms of political government through variants of prisoner's dilemma. Monarchy authority explained by recognition each citizen expects others view king as person whose orders will be followed since coordinating communication among citizens to replace sovereign barred by crime punishment. Public debate in democracies sends clear reliable information regarding intentions to other states while difficult knowing nondemocratic leaders' intentions creating mistrust unwillingness to make concessions. War may result from asymmetric information when countries misrepresent military resources rendering them unable settle disputes agreeably without fighting. Commitment problems arise when two countries wish settling dispute peacefully but each wishes going back on terms forcing resort to warfare. Issue indivisibilities also cause wars according to Peter John Wood's 2013 research looking into nations reducing climate change through treaties creating prisoner's dilemma for participating nations. Defence science and technology applications focus on Command and Control Warfare including Resource Allocation Warfare, Information Warfare, Weapons Control Warfare, and Adversary Monitoring Warfare. Surface ships tracking hostile submarines and submarines evading detection demonstrate interdependent decision-making regarding bearing speed sensor technology activated by both vessels. Stackelberg equilibrium analysis automates transformation public vulnerability data into models allowing defenders synthesize optimal defence strategies enhancing cyber resilience enabling anticipating countering attackers best responses.
Nobel Laureates And Academic Recognition
John Maynard Smith received Crafoord Prize for applying evolutionary game theory in 1999 recognizing contributions to biological applications of the field. Fifteen game theorists won Nobel Memorial Prize in Economic Sciences as of 2020 including most recently Paul Milgrom and Robert B. Wilson. Nash Selten and Harsanyi became Economics Nobel Laureates in 1994 for contributions to economic game theory. Thomas Schelling and Robert Aumann followed them as Nobel Laureates in 2005 working on dynamic models early examples of evolutionary game theory and equilibrium school respectively. Leonid Hurwicz Eric Maskin Roger Myerson awarded Nobel Prize in Economics in 2007 laying foundations mechanism design theory with Myerson contributing proper equilibrium notion important graduate text Game Theory Analysis of Conflict. Alvin E. Roth Lloyd S. Shapley received Nobel Prize in Economics in 2012 for stable allocations theory practice market design. Jean Tirole won Nobel Prize in 2014 continuing recognition of game theory's academic importance across decades. These awards highlight how mathematical models of strategic interactions evolved from probability studies into essential tools understanding human animal computer behaviors across economics biology politics defense science technology.