H. Peyton Young | |
---|---|

Born | March 9, 1945 |

Nationality | American |

Alma mater | North Shore Country Day School Harvard University University of Michigan |

Known for | Evolutionary Game Theory Social Dynamics Learning in Games Social Norms Distributive justice Applications of Game Theory to Finance |

Awards | George Hallett Award, American Political Science Association Lester R. Ford Award, Mathematical Association of America |

Scientific career | |

Fields | Economics, Game Theory, Finance |

Institutions | London School of Economics University of Oxford Nuffield College, Oxford U.S. Department of the Treasury |

Doctoral advisor | Thomas Frederick Storer Jack Edmonds |

**Hobart Peyton Young** (born March 9, 1945) is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury.

- Education and career
- Contributions
- Evolutionary game theory
- Learning in games
- Social Norms
- The Diffusion of Innovations
- Shapley value
- The Kemeny-Young Method
- References and Selected papers
- Books
- References
- External links

Peyton Young was named a fellow of the Econometric Society in 1995, a fellow of the British Academy in 2007, and a fellow of the American Academy of Arts and Sciences in 2018. He served as president of the Game Theory Society from 2006–08. He has published widely on learning in games, the evolution of social norms and institutions, cooperative game theory, bargaining and negotiation, taxation and cost allocation, political representation, voting procedures, and distributive justice.

In 1966, he graduated cum laude in general studies from Harvard University. He completed a PhD in Mathematics at the University of Michigan in 1970, where he graduated with the Sumner B. Myers thesis prize for his work in combinatorial mathematics.

His first academic post was at the graduate school of the City University of New York as assistant professor and then associate professor, from 1971 to 1976. From 1976 to 1982, Young was research scholar and deputy chairman of the Systems and Decision Sciences Division at the Institute for Applied Systems Analysis, Austria. He was then appointed professor of Economics and Public Policy in the School of Public Affairs at the University of Maryland, College Park from 1992 to 1994. Young was Scott & Barbara Black Professor of Economics at the Johns Hopkins University from 1994, until moving to Oxford as James Meade Professor of Economics in 2007. He has been centennial professor at the London School of Economics since 2015 and remains a professorial fellow of Nuffield College, Oxford.

Conventional concepts of dynamic stability, including the * evolutionarily stable strategy * concept, identify states from which small once-off deviations are self-correcting. These stability concepts are not appropriate for analyzing social and economic systems which are constantly perturbed by idiosyncratic behavior and mistakes, and individual and aggregate shocks to payoffs. Building upon Freidlin and Wentzell's (1984) theory of large deviations for continuous time-processes, Dean Foster and Peyton Young (1990) developed the more powerful concept of *stochastic stability*: "The stochastically stable set [SSS] is the set of states such that, in the long run, it is nearly certain that the system lies within every open set containing S as the noise tends slowly to zero" [p. 221]. This solution concept created a major impact in economics and game theory after Young (1993) developed a more tractable version of the theory for general finite-state Markov chains. A state is stochastically stable if it attracts positive weight in the stationary distribution of the Markov chain. Young develops powerful graph-theoretic tools for identifying the stochastically stable states.

In an influential book, *Individual Strategy and Social Structure*, Young provides a clear and compact exposition of the major results in the field of stochastic evolutionary game theory, which he pioneered. He introduces his model of social interactions called 'adaptive play.' Agents are randomly selected from a large population to play a fixed game. They choose a myopic best response, based upon a random sample of past plays of the game. The evolution of the (bounded) history of play is described by a finite Markov chain. Idiosyncratic behavior or mistakes constantly perturb the process, so that every state is accessible from every other. This means that the Markov chain is ergodic, so there is a unique stationary distribution which characterizes the long-run behavior of the process. Recent work by Young and coauthors finds that evolutionary dynamics of this and other kinds can transit rapidly to scholastically stable equilibria from locally stable ones, when perturbations are small but nonvanishing (Arieli and Young 2016, Kreindler and Young 2013, Kreindler and Young 2014).

The theory is used to show that in 2x2 coordination games, the risk-dominant equilibrium will be played virtually all the time, as time goes to infinity. It also yields a formal proof of Thomas Schelling's (1971) result that residential segregation emerges at the social level even if no individual prefers to be segregated. In addition, the theory "demonstrates how high-rationality solution concepts in game theory can emerge in a world populated by low-rationality agents" [p. 144]. In bargaining games, Young demonstrates that the Nash (1950) and Kalai-Smorodinsky (1975) bargaining solutions emerge from the decentralized actions of boundedly rational agents without common knowledge.

Whereas evolutionary game theory studies the behavior of large populations of agents, the theory of *learning in games* focuses on whether the actions of a small group of players end up conforming to some notion of equilibrium. This is a challenging problem, because social systems are self-referential: the act of learning changes the thing to be learned. There is a complex feedback between a player's beliefs, their actions and the actions of others, which makes the data-generating process exceedingly non-stationary. Young has made numerous contributions to this literature. Foster and Young (2001) demonstrate the failure of Bayesian learning rules to learn mixed equilibria in games of uncertain information. Foster and Young (2003) introduce a learning procedure in which players form hypotheses about their opponents' strategies, which they occasionally test against their opponents' past play. By backing off from rationality in this way, Foster and Young show that there are natural and robust learning procedures that lead to Nash equilibrium in general normal form games.

The recent literature on learning in games is elegantly reviewed in Young's 2004 book, *Strategic Learning and its Limits*.

In a series of papers, Young has applied the techniques of stochastic evolutionary game theory to the study of social norms (see Young 2015 for a review). The theory identifies four key features of norm dynamics.

(1) *Persistence*: once norms are in place, they persist for long periods of time despite changing external conditions.

(2) *Tipping*: when norms change, they do so suddenly. Deviations from an established norm may occur incrementally at first. Once a critical mass of deviators forms, however, the process tips and a new norm spreads rapidly through the population.

(3) *Compression*: norms imply that behavior (e.g. retirement ages, cropsharing contracts) exhibits a higher degree of conformity and lower responsiveness to economic conditions than predicted by standard economic models.

(4) *Local conformity/global diversity*: A norm is one of many possible equilibria. Compression implies that individuals who are closely connected conform fairly closely to a particular norm. At the same time, the presence of multiple equilibria implies that less closely connected individuals in the population could arrive at a very different norm.

These predictions are borne out in empirical work. Several regularities were uncovered in Young and Burke's (2001) study of cropsharing contracts in Illinois, which made use of detailed information on the terms of contracts on several thousand farms from different parts of the state. Firstly, there was considerable compression in the contract terms: 98% of all contracts involved 1/2-1/2, 2/5-3/5 or 1/3-2/3 splits. Secondly, when splitting the sample into farms from Northern and Southern Illinois, Young and Burke discovered a high degree of uniformity in contracts within each region, but significant variance across regions---evidence of the local conformity/global diversity effect. In Northern Illinois, the customary share was 1/2-1/2. In Southern Illinois, it was 1/3-2/3 or 2/5-3/5.

Young has also made significant applied contributions to understanding the diffusion of new ideas, technologies and practices in a population. The spread of particular social norms can be analyzed within the same framework. In the course of several papers (Young 2003, Young 2011, Kreindler and Young 2014), Young has showed how the topology of a social network affects the rate and nature of diffusion under particular adoption rules at the individual level.

In an influential 2009 paper, Young turned attention to the diffusion dynamics that can result from different adoption rules in a well-mixed population. In particular, he distinguished between three different classes of diffusion model:

(1) *Contagion*: Individuals adopt an innovation (a new idea, product or practice) following contact with existing adopters.

(2) *Social Influence*: Individuals are likely to adopt an innovation when a critical mass of individuals in their group has adopted it.

(3) *Social Leaning*: Individuals observe the payoffs of adopters and adopt the innovation when these payoffs are sufficiently high.

The third adoption process is most closely related to optimizing behavior and thus standard approaches in economics. The first two processes are, however, the ones focused on by the vast sociological and marketing literature on the subject.

Young characterized the mean dynamic of each of these processes under general forms of heterogeneity in individual beliefs and preferences. While each of the dynamics yields a familiar S-shaped adoption curve, Young showed how the underlying adoption process can be inferred from the aggregate adoption curve. It turns out that each process leaves a distinct footprint. Turning to data on hybrid corn adoption in the United States, Young presented evidence of superexponential acceleration in the early stages of adoption, a hallmark of social learning.

Young (1985) has contributed an axiomatization of the Shapley value. It is regarded as a key piece^{ [1] } for understanding the relationship between the marginality principle and the Shapley value. Young shows that the Shapley value is the only symmetric and efficient solution concept that is solely computed from a player's marginal contributions in a cooperative game. Consequently, the Shapley value is the only efficient and symmetric solution that satisfies monotonicity which requires that whenever a player's contribution to all coalitions weakly increases, then this player's allocation should also weakly increase. This justifies the Shapley value as *the* measure of a player's productivity in a cooperative game and makes it particularly appealing for cost allocation models.^{ [2] }^{ [3] }

The ** Kemeny–Young method ** is a voting system that uses preferential ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.

The Kemeny–Young method was developed by John Kemeny in 1959. Young and Levenglick (1978) showed that this method was the unique neutral method satisfying reinforcement and the Condorcet criterion. In other papers (Young 1986, 1988, 1995, 1997), Young adopted an epistemic approach to preference-aggregation: he supposed that there was an objectively 'correct', but unknown preference order over the alternatives, and voters receive noisy signals of this true preference order (cf. Condorcet's jury theorem). Using a simple probabilistic model for these noisy signals, Young showed that the Kemeny–Young method was the maximum likelihood estimator of the true preference order. Young further argues that Condorcet himself was aware of the Kemeny-Young rule and its maximum-likelihood interpretation, but was unable to clearly express his ideas.

- J. Kemeny, "Mathematics without numbers",
*Daedalus*,**88**(1959), 577–591. - H. P. Young and A. Levenglick, "A Consistent Extension of Condorcet's Election Principle",
*SIAM Journal on Applied Mathematics***35**, no. 2 (1978), 285–300. - H. P. Young, "Optimal ranking and choice from pairwise comparisons", in
*Information pooling and group decision making*edited by B. Grofman and G. Owen (1986), JAI Press, 113–122. - H.P Young, "Monotonic solutions of cooperative games",
*International Journal of Game Theory*,**14**, No. 2 (1985), 65–72. - H. P. Young, "Condorcet's Theory of Voting",
*American Political Science Review***82**, no. 2 (1988), 1231–1244. - D. Foster and H.P Young, "Stochastic Evolutionary Game Dynamics",
*Theoretical Population Biology*,**38**(1990), 219–232. - H.P Young, "The Evolution of Conventions",
*Econometrica*,**61**(1993), 57–84. - H.P Young, "An Evolutionary Model of Bargaining",
*Journal of Economic Theory*,**59**(1993), 145–168. - H. P. Young, "Optimal Voting Rules",
*Journal of Economic Perspectives***9**, no.1 (1995), 51–64. - H. P. Young, "Group choice and individual judgements", Chapter 9 of
*Perspectives on public choice: a handbook*, edited by Dennis Mueller (1997) Cambridge UP., pp. 181–200. - D. Foster and H.P Young, "On the Impossibility of Predicting the Behavior of Rational Agents",
*Proceedings of the National Academy of Sciences of the USA*,**98**, no. 22 (2001), 12848–12853. - H.P Young and M.A. Burke, "Competition and Custom in Economic Contracts: A Case Study of Illinois Agriculture",
*American Economic Review*,**91**(2001), 559–573. - D. Foster and H.P Young, "Learning, Hypothesis Testing, and Nash Equilibrium",
*Games and Economic Behavior*,**45**(2003), 73–96. - H.P Young, "The Diffusion of Innovations in Social Networks” in
*The Economy as a Complex Evolving System*, vol. III, Lawrence E. Blume and Steven N. Durlauf, eds. Oxford University Press, (2003). - H.P Young, "Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence and Social Learning",
*American Economic Review*,**99**(2009), 1899–1924. - H.P Young, "Learning by Trial and Error",
*Games and Economic Behavior*,**65**(2009), 626–643. - D. Foster and H.P Young, "Gaming Performance Fees by Portfolio Managers",
*Quarterly Journal of Economics*,**125**(2010), 1435–1458. - H.P Young, "The Dynamics of Social Innovation”,
*Proceedings of the National Academy of Sciences*,**108**, No. 4 (2011), 21285–21291. - B.S.R. Pradelski and H.P Young, "Learning Efficient Nash Equilibria in Distributed Systems",
*Games and Economic Behavior*,**75**(2012), 882–897. - G. Kreindler and H.P Young, "Fast Convergence in Evolutionary Equilibrium Selection",
*Games and Economic Behavior*,**80**(2013), 39–67. - G. Kreindler and H.P Young, "Rapid Innovation Diffusion in Social Networks",
*Proceedings of the National Academy of Sciences*,**111 Suppl 3**(2014), 10881–10888. - H.P Young, "The Evolution of Social Norms",
*Annual Review of Economics*,**7**(2015), 359–87. - I. Arieli and H.P Young, "Stochastic Learning Dynamics and Speed of Convergence in Population Games",
*Econometrica*,**84**(2016), 627–676.

- H. Peyton Young (2004).
*Strategic Learning and Its Limits*. Oxford UK: Oxford University Press. Contents and introduction. - _____ (2001).
*Fair Representation*, 2nd edition (with M. L. Balinski). Washington, D. C.: The Brookings Institution. Contents and introduction.^{[ permanent dead link ]} - _____ (1998).
*Individual Strategy and Social Structure: An Evolutionary Theory of Institutions*. Princeton, NJ: Princeton University Press. Contents and introduction.^{[ permanent dead link ]} - _____ (1994).
*Equity: In Theory and Practice*. Princeton NJ: Princeton University Press. Contents and introduction.^{[ permanent dead link ]}

An **evolutionarily stable strategy** (**ESS**) is a strategy that is *impermeable* when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy which may be novel or initially rare. Introduced by John Maynard Smith and George R. Price in 1972/3, it is an important concept in behavioural ecology, evolutionary psychology, mathematical game theory and economics, with applications in other fields such as anthropology, philosophy and political science.

**Game theory** is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. In the 21st century, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

**Social dynamics** is the study of the behavior of groups that results from the interactions of individual group members as well to the study of the relationship between individual interactions and group level behaviors.

**Social norms** are shared expectations of acceptable behavior by groups. Social norms can both be informal understandings that govern the behavior of members of a society, as well as be codified into rules and laws. Institutions are composed of multiple norms. Norms are shared and social beliefs about behavior; thus, they are distinct from "ideas", "attitudes", and "values", which can be held privately, and which do not necessarily concern behavior. Norms are contingent on context, social group, and historical circumstances.

**Evolutionary economics** is part of mainstream economics as well as a heterodox school of economic thought that is inspired by evolutionary biology. Much like mainstream economics, it stresses complex interdependencies, competition, growth, structural change, and resource constraints but differs in the approaches which are used to analyze these phenomena.

**Experimental economics** is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law.

**Lloyd Stowell Shapley** was an American mathematician and Nobel Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design."

In game theory, **fictitious play** is a learning rule first introduced by George W. Brown. In it, each player presumes that the opponents are playing stationary strategies. At each round, each player thus best responds to the empirical frequency of play of their opponent. Such a method is of course adequate if the opponent indeed uses a stationary strategy, while it is flawed if the opponent's strategy is non-stationary. The opponent's strategy may for example be conditioned on the fictitious player's last move.

**Kenneth George "Ken" Binmore**, is an English mathematician, economist, and game theorist, a Professor Emeritus of Economics at University College London (UCL) and a Visiting Emeritus Professor of Economics at the University of Bristol. As a founder of the modern economic theory of bargaining, and has made important contributions to the foundations of game theory, experimental economics, and evolutionary game theory, and to analytical philosophy. Binmore took up economics after a career in mathematics, in which he held the Chair of Mathematics at the London School of Economics. Since his switch he has been at the forefront of developments in game theory. His other research interests include political and moral philosophy, decision theory, and statistics. He is the author of over 100 scholarly papers and 14 books.

**David Knudsen Levine** is department of Economics and Robert Schuman Center for Advanced Study Joint Chair at the European University Institute; he is John H. Biggs Distinguished Professor of Economics Emeritus at Washington University in St. Louis. His research includes the study of intellectual property and endogenous growth in dynamic general equilibrium models, the endogenous formation of preferences, social norms and institutions, learning in games, and game theory applications to experimental economics.

**Martin Shubik** was an American economist, who was Professor Emeritus of Mathematical Institutional Economics at Yale University.

**Quantal response equilibrium** (**QRE**) is a solution concept in game theory. First introduced by Richard McKelvey and Thomas Palfrey, it provides an equilibrium notion with bounded rationality. QRE is not an equilibrium refinement, and it can give significantly different results from Nash equilibrium. QRE is only defined for games with discrete strategies, although there are continuous-strategy analogues.

**Risk dominance** and **payoff dominance** are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. A Nash equilibrium is considered **payoff dominant** if it is Pareto superior to all other Nash equilibria in the game. When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered **risk dominant** if it has the largest basin of attraction. This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it.

In game theory, a **stochastically stable equilibrium** is a refinement of the evolutionarily stable state in evolutionary game theory, proposed by Dean Foster and Peyton Young. An evolutionary stable state S is also stochastically stable if under vanishing noise the probability that the population is in the vicinity of state S does not go to zero.

**Pradeep Dubey** is an Indian game theorist. He is Professor of Economics at State University of New York, Stony Brook and a member of the Stony Brook Center for Game Theory. He also holds a visiting position at Cowles Foundation, Yale University. He did his schooling from the St. Columba's School, Delhi. He received his Ph.D. in Applied Mathematics from Cornell University and B.Sc. from the University of Delhi. His areas of research interests are game theory and mathematical economics. He has published, among others, in *Econometrica*, *Games and Economic Behavior*, *Journal of Economic Theory* and *Quarterly Journal of Economics*. He is a Fellow of *The Econometric Society* and a member of the council of *Game Theory Society*.

**Algorithmic game theory (AGT)** is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments.

**Ehud Kalai** is a prominent Israeli American game theorist and mathematical economist known for his contributions to the field of game theory and its interface with economics, social choice, computer science and operations research. He was the James J. O’Connor Distinguished Professor of Decision and Game Sciences at Northwestern University, 1975-2017, and currently is a Professor Emeritus of Managerial Economics and Decision Sciences.

**Jean-François Mertens** was a Belgian game theorist and mathematical economist.

**Maximal lotteries** refers to a probabilistic voting system first considered by the French mathematician and social scientist Germain Kreweras in 1965. The method uses preferential ballots and returns so-called maximal lotteries, i.e., probability distributions over the alternatives that are weakly preferred to any other probability distribution. Maximal lotteries satisfy the Condorcet criterion, the Smith criterion, reversal symmetry, polynomial runtime, and probabilistic versions of reinforcement, participation, and independence of clones.

- ↑ Geoffroy De Clippel Roberto Serrano (2008). "Marginal Contributions and Externalities in the Value".
*Econometrica*.**76**(6): 1413–1436. CiteSeerX 10.1.1.388.1120 . doi:10.3982/ECTA7224. - ↑ Casajus, André; Huettner, Frank (2014). "Weakly monotonic solutions for cooperative games".
*Journal of Economic Theory*.**154**: 162–172. doi:10.1016/j.jet.2014.09.004. - ↑ Nagarajan, Mahesh; Sošić, Greys (2008). "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions".
*European Journal of Operational Research*.**187**(3): 719–745. doi:10.1016/j.ejor.2006.05.045. ISSN 0377-2217.

- Young's page at the University of Oxford with his CV and full list of publications.
- Peyton Young at the Mathematics Genealogy Project

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