Evolutionary Game Theory and Behavioral Economics

Introduction

With the increasing importance of mathematics in economics approaches, our project is to focus on the application of quantitative science to behavioral economics. Specifically, we will investigate the more sophisticated tools needed to develop more complicated economic models as the economic thoughts evolve. The economic paradigms of interest are the Walrasian paradigm, which dominated in the third quarter of the 20th century, and another economic paradigm which we refer to as “Bowles’ paradigm” for the sake of easy distinction (it does not necessarily mean that Samuel Bowles invented this paradigm).

We will first analyze Walrasian’s paradigm and the mathematics behind it. Then, we will point out some of its shortage, i.e. things that the model cannot explain. Finally, we will use the game theoretical approach of Bowles’s paradigm to explain those.

3 empirically observed characteristics

1. Social interaction

2. Individual behaviors

3. Technologies

- Non-contractual social interactions: when individuals interact, it is the exception, not the rule, that everything between them is regulated by an enforced contract

- Want to analyze the coordination problems in order to see how institutions work - institutions and participants in the interaction

- Believes that Walrasian paradigm is inferior to the more elaborate modeling of institutions by game theory

- Main objective in this chapter is to introduce basic game theory to provide taxonomy of social interactions and their outcomes

- Prisoner’s dilemma- each individual act to maximize their pay off but when both choose to maximize their payoff, the outcome is worse for both

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Necessary Backgrounds

a. Classical Game Theory

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Game Theory

Game Theory is a way of modeling of strategic interactions, which means the consequences of each individual's actions are dependent on the actions taken by others and it requires detailed attention to the institutional environment in which the game takes place.

Classical Game Theory

- Forward-looking cognitive evaluations by the players

- Two main solution concepts: Dominance (process of elimination) and Nash equilibrium (may be one or more outcome that no individual has any incentive to change his strategy based on the strategies taken by all the others)

- These two solutions are based on a best response strategy

b. Evolutionary Game Theory

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- "game theory makes less progress with non-cooperative n-person interactions, but it addresses complex human interaction; what makes interaction difficult is the assumption that they act strategically rather than taking the other’s actions as given"

- Walrasian case – competitive markets for goods governed by complete contracts, strategic actions, only equilibrium trade takes place; single interacting with a given set of prices, technological blueprints and constraints

- But we will see that there are many more important interactions: labor markets, credit markets, markets for information and goods of variable quality

Evolutionary game theory typically assumes that individuals have limited information about the consequences of their actions, and that they update their beliefs by trial-and-error methods using local knowledge based on their own and others recent past experience; subjects in games are “intellectually challenged” and backward looking, but classical theory opposite

- Another reason to reject classical game theory is that it assumes equilibrium can be settled solely by game theory itself and ignores history of the players; third: game theory with narrow scope of institutions; society is not well-modeled as a single game, or one with an unchanging structure

- Games are overlapping in reality

- Evolutionary game theory has modified classical game theory to take account of our limited cognitive capacities by positing agents who update their behaviors using imperfectly observed local info.

- Both evolutionary game theory and models of cultural evolution describe the interactions of adaptive agents, eschewing both the zero-intelligence agents of the standard biological models and the highly cognitive agents of the standard biological models and the highly cognitive agents of classical game theory

- Evolutionary approach: modeling of chance, differential replication, out of equilibrium dynamics, and population structure (p.61)

- Gene-behavior correspondence

- Cultural traits learned rather than transmitted genetically

- Evolutionary modeling characteristic: populations are structured hierarchically and differential replication can take place at more than one level; process of differential replication is typically taking place at many levels simultaneously: within individuals, among individuals, among groups and so on

c. Others

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Hawk Dove Game: commonly applied to culturally or genetically transmitted human behavioral traits such as aggression and sharing, but it was initially developed to study contests among other animals

- When doves meet they share a prize, whereas when hawks meet they fight over the prize, inflicting costs on one another, and when a Hawk meets a Dove, the Hawk takes the prize (p.79) Table 2.2 (Hawks vs Hawks = 1/3; Dove vs Dove = divide evenly without cost)

- pp.80 – 87 (Hawk Dove formulas and explanations)

- The equal payoff condition defining stationary of p makes it clear that p* is Nash equilibrium

- If there is only one strategy to replicate, a population frequency governed by a replicator dynamic will remain unchanged

- p* = v/c is not a desirable outcome based on Hawk Dove Game; average payoff is when p=0 when there are no hawks at all; both are better off the fewer Hawks there are

- Solution: find a way to reduce the number of contested interactions; John Maynard Smith suggested: “if owner plays Hawk, if intruder play Dove” labeled “Bourgeois”

- Ambiguity of possession arise

- Private property rights could have evolved spontaneously

- Institutional crowding out

- Invisible hand arguments are misleading when applied to institutions and behavioral traits

Edgeworth Box: [1]

"The Edgeworth box has a central position in neoclassical economics. It is used to show that in unfettered markets, in which agents pursue self-interests, exchanges must end up on the contract curve that represent equilibrium outcomes.

The Walrasian general equilibrium theory was one of the most elaborate expositions of the neoclassical paradigm. The theory hypothesized that the principle of marginality could be used to prove that the price mechanism, under the standard neoclassical set of assumed ideal conditions, was capable of clearing all markets and, consequently, lead to the emergence of a general market equilibrium.

The goal of all economic activity is to provide utility for its participants. The Walrasian general equilibrium theory was mainly concerned with the question of prices as a clearing mechanism, and not so much with the utility aspect. This was in line with the general trend of the neoclassical period, which saw the questions of how welfare and wider social goals connected to the economic processes pushed to the background.

However, the social goals, which all exchanges also pursue, means that this is not necessarily the case. This can be shown by adding depictions of social optima zones, within which exchanges that pursue goals beyond the laissez-faire assumption of unbridled self-interests can fall." (Sandbec)

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Walrasian paradigm

assumes that individuals choose actions based on the far-sighted evaluation of their consequences based on preferences that are self-regarding and exogenously determined

social interactions take the exclusive form of contractual exchanges

that increasing returns to scale can be ignored in most applications and institutions do not evolve

institutions exist to facilitate trade

represents economic behavior as the solution to a constrained optimization problem faced by a fully informed individual in a virtually institution-free environment

Deduced a few strong predictions concerning the outcomes likely to be observed in the economy

- The two traditions: constitutional and evolutionary deploy different analytical techniques and distinct metaphors such as “institutions”

- Walrasian general equilibrium model and population-level models depicting evolutionary dynamics of biological systems under the combined influences of chance, inheritance, and natural selection

Similarities: both model systems of competition in which practices or designs with higher payoffs increase quickly

Differ: model of the process of heritable innovation based on mutation and recombination, but economics has no generally accepted theory of innovation; misses the important fact that humans produce novelty intentionally and often through collective actions and not simply by chance

The Theory of General Equilibrium[2]

"General equilibrium refers to the idea that divergent interests of consumers and producers can be harmonized not only for single markets, but also for all markets simultaneously (3). Walras’ primary work, the Elements, created a scenario for general equilibrium, a scenario that was perfected throughout his following three editions. The quintessential nature of the Elements was, and continues to be, a theory of social wealth (1). His classification of social wealth divided durable goods, or capital, from non-durable goods, or income. Capital included land, personal faculties and capital goods proper, which could be used more than once in its purpose (2). Income, in turn, could only be used once, after which it no longer existed. According to Jaffe, Walras referred to each successive use of capital as a “service”, which was passed to the category of income due to it non-durable nature. The fundamental necessity of money was injected into the scenario by separating it into two categories due to its mixed nature of durability and non-durability. As cash holdings in circulation, for instance, money was considered a capital good, but for money as savings, it was considered a form of income (2)." [3]

+ Hicksian programme "refers to the incorporation of "Grand Themes" like stability, uncertainty, money, capital, macroeconomics, growth, etc. into general equilibrium theory, the project effectively initiated by John Hicks in Value and Capital (1939) which, in turn, harked back to the grand vision set out in Léon Walras's Elements of Pure Economics (1874). The mathematics employed in this time period were of a different hue and in some ways simpler, not going much beyond differential equations and linear algebra. In this sense, there was a temporary return to the "Paretian" type of general equilibrium theory."

+ Edgeworthian programme "refers to the efforts to examine the relationship between a Walrasian competitive equilibrium and the solutions obtained via alternative exchange process (notably those from game theory). The mathematical tools of choicethat were introduced in this effort in the 1960s and 1970s -- i.e. measure theory and non-standard analysis -- were substantially more demanding than anything most economists had been used to."

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Theoretical Institutional Economics (Bowles’ paradigm)

Bowles’ paradigm assumes non-contractual social interactions, adaptive and other-regarding behaviors, and generalized increasing returns.

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The model of labor market

Work effort cannot be contracted for because information concerning an employee’s effort is known to the employer at best very imperfectly and is not verifiable

Employer-employee interaction The employer knows the workers best effort response, e (w, m; z) At the beginning of a period, the employer selects and announces a termination probability and over the economically relevant ranges; a wage rate, w; and a level of monitoring per hour of labor hired m. Following the employers announcement of her effort-incentive strategy, and hence knowing the above, the worker selects e so as to maximize his present value of a lifetime utility At the end of the period, the worker is paid and experiences the utility he incurs as a result of his effort and pay, and his employment is renewed or terminated, the later occurring with probability t(e, m)

Models based on incomplete contracting for effort or other aspects of the labor exchange explain how a competitive equilibrium could exhibit involuntary unemployment

During this process the standard theories of the labor market and the firm have been transformed

The importance of reciprocity motives and other social preferences in explaining why firms do not sell jobs underlines the futility of simply introducing incomplete contracting into an otherwise unaltered Walrasian framework

If the difficulty of monitoring labor effort differs across technologies, the choice of technology will be influenced by the nature of the labor discipline problem

Such aspects of the labor discipline environment as prevailing norms, whether terminated workers have access to unemployment insurance, and other influences on the worker’s effort choice, will affect the profitability of alternative technologies

This view goes against the standard model where the choice of technology responds to factor scarcities that are indicated by factor prices

Technologies and institutions co evolve and influence the development of the other

Second labor market

Other sectors of the economy characterized by insecure employment, short job ladders, and low wages make up the secondary labor market

Why is power associated with some factors of production and not others?

Marx-Coase-Simon theory of employment relationship Social preferences play an important part in determining outcomes The firm is represented as a group of suppliers of inputs to a common production process whose activities are coordinated by means of an authority structure rather than by market exchanges governed by complete contracts The distribution of behavioral types in a population that influences the equilibrium distribution of contracts

The way that rights of control over assets and claims on the residual income of assets are assigned to particular individuals

Unconventional social preferences assume special importance in nonmarket interactions and in market exchanges governed by incomplete contracts

Where contracts are incomplete, exchange is often facilitated when traders discriminate in favor of insiders and engage in parochial practices

In the walrasian paradigm these exchange supporting interaction structures are called “market imperfections” and are opposed as impediments to “flexibility”

Work effort cannot be contracted for because information concerning an employee’s effort is known to the employer at best very imperfectly and is not verifiable

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References

(1) Bowles, Samuel. Microeconomics: Behavior, Institutions, and Evolution. Princeton, NJ: Princeton University Press, 2006. Print.

(2) Gintis, Herbert. Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction. 1st ed. Princeton, NJ: Princeton University Press, 2000. Print.

(3) Gintis, Herbert. The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton, NJ: Princeton University Press, 2009. Print.

(4) Hirshleifer, Jack. Price Theory and Applications. 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1980. 192-7. Print.

(5) Sandbec, Dix. "The Edgeworth Box beyond Laissez-faire." International Journal of Green Economics1.3 (2007): n. pag. Web. 13 Apr 2011. <http://dixsandbeck.ca/pdf/edgebox.pdf>.