School of Economics

 

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Dr Edward Cartwright

Reader in Economics

School of Economics, Keynes College, B1.06

Edward Cartwright is Director of Graduate Studies (PhD programmes)

About

Edward Cartwright is Reader in Economics. He gained a BA in mathematics and economics at the University of Durham and an MSc and PhD in economics at the University of Warwick. He subsequently spent a year as a post-doctoral student at Université Paris 1, Panthéon-Sorbonne before joining the University of Kent in 2004.

Edward’s main research interests are game theory, behavioural economics and public economics. His current work focuses on threshold public good games, large games, the consequences and origins of conformity and prejudice, and leadership in coordination games. Edward is associate editor at the Journal of Public Economic Theory.

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Publications

Edward's publications can also be found on RePEc, Orcid and ResearchGate.

Also view these in the Kent Academic Repository
Articles

    Alberti, Federica and Cartwright, Edward (2015) Does the Endowment of Contributors Make a Difference in Threshold Public Games? Finanz Archiv. ISSN 0015-2218. (in press)

    Abstract

    We investigate experimentally whether the endowment of potential contributors changes outcomes in threshold public good games. We find that the variance in contributions is significantly reduced for low and high levels of endowment when compared to an intermediate level of endowment. This difference emerges with experience. Evidence on whether the level of endowment influences the success rate at providing public goods is more mixed. We provide, however, a measure of endowment size that correlates with success rate. Our interpretation suggests that people find it hardest to coordinate on the provision of threshold public goods when endowments are of intermediate size. By intermediate we mean that the endowment is small enough that people need to contribute relatively a lot to fund the good, but also large enough that no one person is critical in providing the good.

    Cartwright, Edward (2015) Strategic delay and information cascades. Journal of Economics-Zeitschrift Fur Nationalokonomie, 114 (1). pp. 63-74. ISSN 0931-8658.

    Abstract

    In a setting where agents must choose between two investments, Zhang (in RAND J Econ 28:188–205, 1997) proposed an equilibrium in which there is strategic delay. This equilibrium relied upon there being an information cascade. We shall demonstrate that an information cascade need not generally occur. It will only occur if and only if the cost of investing takes relatively extreme values. Taking this into account we derive a revised equilibrium that is still characterized by strategic delay.

    Cartwright, Edward and Menezes, Matheus L.C. (2014) Cheating to win: Dishonesty and the intensity of competition. Economics Letters, 122 (1). pp. 55-58. ISSN 0165-1765.

    Abstract

    We argue that the intensity of competition within a group or organization can have an important influence on whether or not people cheat. To make this point we first work through a simple model of strategic misreporting in the workplace. For low and high levels of competition we show that, in equilibrium, few are predicted to misreport. It is for medium levels of competition that misreporting is predicted to be highest. We test this prediction experimentally and find good support for it. This finding has implications for the design of incentive structures within groups and organizations.

    Cartwright, Edward and Wooders, Myrna (2014) Correlated equilibrium, conformity and stereotyping in social groups. Journal of Public Economic Theory, 16 (5). pp. 743-766. ISSN 1097-3923.

    Abstract

    We argue that a social norm and the coordination of behavior within social groups can be expressed by a correlated equilibrium. Given a social group structure (a partition of individuals into social groups), we propose four conditions that one may expect of a correlated equilibrium consistent with social norms. These are: (a) within-group anonymity (conformity within groups), (b) group independence (no conformity between groups), (c) homophily (individuals in the same group have similar attributes), and (d) predictable group behavior (ex-post stability). We demonstrate that correlated equilibrium satisfying (a)-(c) exist very generally and equilibrium satisfying (a)-(d) exist in games with many players. We also consider stereotyped beliefs - beliefs that all individuals in a social group can be expected to behave in the same way - and show that stereotyping is not costly to the person who stereotypes but may or may not be beneficial to society.

    Cartwright, Edward and Lovett, Denise (2014) Conditional cooperation and the marginal per-capita return in public good games. Games, 5 (4). pp. 234-256. ISSN 2073-4336.

    Abstract

    We investigate experimentally whether the extent of conditional cooperation in public good games depends on the marginal per capita return (MPCR) to the public good and type of game. The MPCR is varied from 0.2 to 0.4 to 0.8. The ‘standard’ game, in which three players contribute before a follower, is compared with a leader-follower game, in which one player leads and three follow. Even though we observe less conditional cooperation for an MPCR of 0.2, the prevalence of conditional cooperation remains relatively stable to changes in the MPCR and game timing. In contrast, the level of MPCR has a strong effect on unconditional contributions. Our results highlight the critical role played by leaders in a public good game.

    Cartwright, Edward (2014) Imitation and coordination in small world networks. Intelligent systems in accounting, finance and management, 21 (2). pp. 71-90. ISSN 1099-1174.

    Cartwright, Edward and Patel, Amrish (2013) How category reporting can improve fundraising. Journal of Economic Behavior and Organization, 87. pp. 73-90. ISSN 0167-2681.

    Abstract

    Many fundraisers report donations using categories such as more than £ 1000, more than £ 10,000, etc. One naturally wonders how we should categorise donations and whether categorising raises more than simple uncategorised reporting. To answer these questions, we employ a signalling game framework in which both the donor's donation and his benefits of being in a higher category are determined endogenously. We find that categorised reporting can always improve fundraising. Both high and low category thresholds can increase donations, with prior beliefs determining which is better. While categorising can lead to the existence of a low donation equilibrium, it is less problematic if signalling benefits are low.

    Cartwright, Edward and Gillet, Joris and Van Vugt, Mark (2013) Leadership by Example in the Weak-link Game. Economic Inquiry, 51 (4). pp. 2028-2043. ISSN 1465-7295.

    Abstract

    We investigate the effects of leadership in a four-player weak-link game. A weak-link game is a coordination game with multiple Pareto-ranked Nash equilibria. Because the more efficient equilibria involve a degree of strategic uncertainty groups typically find it difficult to coordinate on more efficient equilibria. We wanted to see whether leadership by example, in the form of one player acting publicly before the rest of the group, could help groups do better. Our results suggest that leadership can increase efficiency but is far from being a guarantee of success. Specifically, in a significant number of groups we observed successful leadership and increased efficiency, but in most groups efficiency was low despite the efforts of leaders. We did not find any difference between voluntary leaders and leaders that are randomly assigned.

    Patel, Amrish and Cartwright, Edward (2012) Naïve Beliefs and the Multiplicity of Social Norms. Journal of Institutional and Theoretical Economics, 168 (2). pp. 280-289. ISSN 0932-4569.

    Abstract

    In a signalling model of conformity, we demonstrate that naïve observers, those that take actions at face value, constrain the set of actions that can possibly be social norms. With rational observers many actions can be norms, but with naïve observers only actions close to that preferred by the ideal type can be norms. We suggest, therefore, that the naïvety or inexperience of observers is an important determinant of norms and how they evolve.

    Cartwright, Edward and Stepanova, Anna (2012) What do Students Learn from a Classroom Experiment: Not much, Unless they Write a Report on it. Journal of Economic Education, 43 (1). pp. 48-57. ISSN 0022-0485.

    Abstract

    The authors ask whether writing a report on a classroom experiment increases a student's performance in an end-of-course test. To answer this question, the authors analyzed data from a first-year undergraduate course based on classroom experiments and found that writing a report has a large positive benefit. They conclude, therefore, that it is important to constructively integrate classroom experiments with some form of assessment or homework in order to realize the maximum benefit from them.

    Gillet, Joris and Cartwright, Edward and Van Vugt, Mark (2011) Selfish or servant leadership? Evolutionary predictions on leadership personalities in coordination games. Personality and Individual Differences, 51 (3). pp. 231-236. ISSN 0191-8869.

    Abstract

    We study the personalities of emergent leaders in two coordination games in groups of four players each with monetary incentives. Our results support the evolutionary hypothesis that leadership is a social good for the group: leadership benefits followers but is potentially costly for the individual taking on the leader role. Across the two economic games leaders do less well – earn less money – on average than followers. Furthermore, social participants choose to lead more often than selfish participants and there is no relationship between leadership behavior and personal dominance. Our results support the idea that leadership can be servant rather than selfish and we note the implications of this finding.

    Alberti, Federica and Cartwright, Edward (2011) Full agreement and the provision of threshold public goods. Jena Economic Research Papers. (submitted)

    Abstract

    We report threshold public good experiments in which group members not only need to be individually willing to contribute enough to provide the public good but also have to agree with each other on what every group members should contribute. We find strong support to the hypothesis that full agreement increases successful provision, although it takes a few repetitions before group members can successfully coordinate. This is consistent with our theoretical results that full agreement works because it increases criticality of each individual decision. The existence of a focal point makes it possible for the group members to successfully coordinate.

    Cartwright, Edward and Patel, Amrish (2010) Imitation and the Incentive to Contribute Early in a Sequential Public Good Game. Journal of Public Economic Theory, 12 (4). pp. 691-708. ISSN 1097-3923.

    Abstract

    Whether motivated by reciprocity or conformity, imitation is common in public good contexts. We consider the incentive for an agent to contribute to a public good if he expects imitation from others. Using a sequential public good game with exogenous ordering, we show that agents early enough in the sequence who believe imitation to be sufficiently likely would want to contribute. By contributing, they expect total contributions to increase significantly. We also show that preferences determine how early an agent need be, that the observed share of imitators in experiments is sufficiently high to warrant contribution and that an increase in group size reduces the incentive to contribute.

    Cartwright, Edward and Patel, Amrish (2010) Public Goods, Social Norms, and Naïve Beliefs. Journal of Public Economic Theory, 12 (2). pp. 199-223. ISSN 1097-3923.

    Abstract

    An individual's contribution to a public good may be seen by others as a signal of attributes such as generosity or wealth. An individual may, therefore, choose their contribution so as to send an appropriate signal to others. In this paper, we question how the inferences made by others will influence the amount contributed to the public good. Evidence suggests that individuals are naïve and biased toward taking things at “face value.” We contrast, therefore, contributions made to a public good if others are expected to make rational inferences versus contributions if others are expected to make naïve inferences.

    Cartwright, Edward and Wooders, Myrna (2009) On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium. International Journal of Game Theory, 38 (1). pp. 127-136. ISSN 0020-7276.

    Abstract

    Treating games of incomplete information, we demonstrate that the existence of an ex post stable strategy vector implies the existence of an approximate Bayesian equilibrium in pure strategies that is also expost stable. Through examples we demonstrate the ‘bounds obtained on the approximation’ are tight.

    Cartwright, Edward and Wooders, Myrna (2009) On equilibrium in pure strategies in games with many players. International Journal of Game Theory, 38 (1). pp. 137-153. ISSN 0020-7276.

    Abstract

    We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can be “?-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on the payoffs of other players.

    Cartwright, Edward (2009) Social norms: Does it matter whether agents are rational or boundedly rational? Journal of Socio Economics, 38 (3). pp. 403-410. ISSN 1053-5357.

    Abstract

    The motivation for this paper is to consider whether changes in conformity over time are likely to depend critically on agent behavior. To get some insight on this we use the framework of Chamley [Chamley, C., 1999. Coordinating regime switches. The Quarterly Journal of Economics 114, 869–905] and compare the dynamic of conformity in a setting where agents are rational to one where they are adaptive (or backward looking). This is followed by a more general discussion on the issue.

    Cartwright, Edward (2009) Conformity and out of equilibrium beliefs. Journal of Economic Behavior and Organization, 70 (1-2). pp. 164-185. ISSN 0167-2681.

    Abstract

    We analyze a model of conformity with contrasting inferences. Given a form of ‘strong inferences’, any non-conforming agent is believed to have ‘extreme preferences’ and can expect to receive low esteem. With a weaker form of inferences, a non-conforming agent could be inferred to have ‘average preferences’ and can expect a smaller fall in esteem. We find that the type of inferences need not influence whether a conformist equilibrium exists. It will, however, impact on the size of the set of conformist equilibria and thus weakening inferences acts as an equilibrium selection device.

    Cartwright, Edward (2007) Imitation, coordination and the emergence of Nash equilibrium. International Journal of Game Theory, 36 (1). pp. 119-135. ISSN 0020-7276.

    Abstract

    We consider a learning dynamic in which players imitate and better reply. Sufficient conditions are provided for Nash equilibrium play to emerge over time. The role of imitation in the learning dynamic is discussed through a series of examples. Most interestingly we demonstrate how imitation can 'help' the emergence of Nash equilibrium where 'more rational' methods do not.

    Cartwright, Edward (2007) Contagion and the Speed of Adjustment in Small Worlds. International Game Theory Review, 9 (4). pp. 689-704. ISSN 0219-1989.

    Abstract

    We model a simple dynamic process in which myopic agents are matched amongst each other to play a coordination game. The network of player interaction is varied between a regular lattice and a random network allowing us to model contagion in small world networks. Weighting times for an equilibrium shift from the risk dominated to risk dominant equilibrium are shown to be smallest in small world networks.

    Cartwright, Edward and Wooders, Myrna and Selten, Reinhard (2006) Behavioural conformity in games with players. Games and Economic Behavior, 57 (2). pp. 347-360. ISSN 0899-8256.

    Abstract

    In the literature of psychology and economics it is frequently observed that individuals tend to conform in their behavior to that of similar individuals. A fundamental question is whether the outcome of such conformity can be consistent with self-interest. We propose that this consistency requires the existence of a Nash or approximate Nash equilibrium that induces a partition of the player set into relatively few societies, each consisting of similar individuals playing similar strategies. In this paper we characterize a family of games admitting the existence of such equilibrium. We also introduce the concept of 'crowding types' into our description of players and distinguish between the crowding type of a player-those characteristics of a player that have direct effects on others-and his tastes. With assumptions of 'within crowding type anonymity' and 'linearity of taste-types' we show that the number of societies can be uniformly bounded.

Books

    Frank, Robert and Cartwright, Edward (2013) Microeconomics and Behaviour. McGraw Hill, 712 pp. ISBN 9780077151546.

    Abstract

    Exploring the relationship between human behaviour and economic analysis, Microeconomics and Behaviour establishes the fundamentals of intermediate microeconomics in a clear and narrative style and develops economic intuition about the world around us. The text continually encourages the reader to think like an economist through the development of core analytical tools and economic naturalist examples.

    Cartwright, Edward (2011) Behavioral Economics. Routledge Advanced Texts in Economics and Finance. Routledge, 478 pp. ISBN 9780415573122.

    Abstract

    This textbook is a first major introduction to behavioral economics, designed primarily for advanced undergraduate students. Unquestionably the hottest new field to have emerged in the social sciences over the past decade, behavioral considerations are now making themselves felt across academia and beyond and books such as Richard Thaler and Cass Sunstein’s Nudge have become blueprints for a new way of thinking. This text will introduce all the key concepts to a student audience. Although grounded in game theory and experimental economics, the focus of the text is very much on Behavior as opposed to Games. The field is presented as a coherent subject and the text covers a host of cutting edge developments including the analysis of fairness, reciprocity and altruism, as well as the brave new frontier of neuroeconomics.

Book Sections

    Cartwright, Edward and Singh, Tarun (2013) Social capital, the culture of trust, and economic development. In: Christiansen, Bryan Economic Behavior, Game Theory, and Technology in Emerging Markets. IGI Global, pp. 91-108. ISBN 9781466647459.

    Abstract

    The benefits accruing from social networks and structures have been shown to correlate with economic performance at both the macro- and micro-levels. Indeed, social capital can be seen as a catalyst through which human and physical capital are utilized and political and economic freedom realized. In this chapter, the authors briefly review the broad extant literature on social capital before embarking in more detail on how game theory can be used to analyze and model social capital. Particular attention is given to the population game approach. This approach is well suited to model social capital as it allows us to capture individual behaviour, societal influence, and network structure. The growth of social capital is seen to depend on the incentives for cooperation, the way in which people learn from past experience, and the inter-connectedness of the social network. A particularly important question for many emerging economies is how social capital can be encouraged to grow from a low base. In a concluding section, which includes a discussion of the complementarities between strong institutions and social capital, the authors use the population game approach to study this issue.

    Cartwright, Edward and Wooders, Myrna and Conley, John (2006) The Law of Demand in Tiebout Economies. In: Fischel, W.A. The Tiebout Model at Fifty: Essays in Public Economics in honor of Wallace Oates. Lincoln Institute of Land Policy, Cambridge, Massachusetts, pp. 273-290. ISBN 1-55844-165-4.

Total publications in KAR: 33 [See all in KAR]

 

 

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Research

Research interests

Much of Edward's current research focuses on aspects of leadership, social learning and social influence. Specifically, it looks to model situations where economic agents are making decisions sequentially or repeatedly and can observe what other agents have done in the past. How are/should agents be influenced by what they observe others doing? and how should an agent behave if he expects others to be influenced by what he is doing?

Particular applications of interest include public good games, coordination games, and large games. Edward's preferred approach is one involving both theory and experiment. Some specific issues that are the subject of ongoing research include:

  • Who chooses to lead, and follow, and why?
  • Does leadership help to resolve coordination problems? If not, what does?
  • The optimal theory of search when agents can learn from the search of others.
  • Does signalling increase giving to public goods/charity?
  • The origins of prejudice and economic discrimination.
  • Ex-post stability and categorization in games with many players.

Current and past research grants that have helped fund this research include:

  • 'An experimental investigation of prejudice and economic discrimination', Nuffield Foundation Small Grant (2009-2011).
  • 'Why some people choose to be leaders: the emergence of leadership in groups and organizations', joint with Mark van Vugt, ESRC Small Grant (2007-2010).
  • 'Anonymous free-riding in collective action problems', joint with Mark van Vugt, British Academy Small Grant (2008-2010).
  • 'Social Learning and the Theory of Search', ESRC First Grant (2006-2007).


Edward is also a member of the University of Kent's Centre for Reasoning and The Centre for the Study of Group Processes.

Edward's RePEc page is http://econpapers.repec.org/RAS/pca11.htm.

Working Papers

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Consultation hours

  • Tue 10.00-11.00
  • Wed 14.00-15.00

 

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PhD supervision

Current students

Former students

  • Dr Amrish Patel (now at University of Gothenburg) (personal page)

 

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Administrative roles

  • Director of Graduate Studies (PhD programmes)

 

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School of Economics, Keynes College, University of Kent, Canterbury, Kent, CT2 7NP

Undergraduate enquiries: +44 (0) 1227 827497, Postgraduate enquiries: +44 (0) 1227 827440 or email us

Last Updated: 19/02/2015