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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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. Economists use game theory in order to speculate outcomes in regards to individual behaviors.

Classical Game Theory

The Walrasian paradigm approaches a classical game theory. It is also known as the conventional game theory. Classical game theory gives emphasis to the idea that the players in the game are forward-looking. There are two main solution concepts used in the classical game theory, which are: Dominance and Nash equilibrium. These two solutions are based on a best response strategy.

(a.) Dominance uses predictions of outcomes in games such as prisoner’s dilemma, in which every player acts according to what other players would do; it is a process of elimination.

(b.) Nash equilibrium’s solution concept to a game, in which it is assumed that each player knows the equilibrium of the other player. Using this knowledge, each player has no incentive or benefit to change their choice. Therefore, the payoffs of their choice are known as the Nash equilibrium. In addition, there are no endogenous source of change because each player are not interested in altering their decision.

Bowel’s critique: Classical game theory assumes that this is the standard way the game will be played. If a player were playing through reasonable play, there is little reason to think that this would lead to Nash equilibrium. Furthermore, not every game has a nash equilibrium and some games have multiple nash equilibria, hence outcomes cannot necessarily be predicted. Classical game theory has addressed this problem of multiple nash equilibria by placing restrictions on player's behavior based on rationality attempting to narrow the possible outcomes. These restrictions were called refinements, which include noncredible threats. These noncredible threats were generally outcomes that were not the best response, or outcomes that resulted without the use of all available information.

Evolutionary Game Theory

Samuel Bowels supports the evolutionary game theory model. The evolutionary game theory typically assumes that individuals have limited information about the consequences of their actions. They update their beliefs by trial-and-error methods using local knowledge based history. In other words, they use past experiences that they have experienced themselves or that they observed from others in order to update their beliefs. In contrast to classical game theory, players in the games are “intellectually challenged” and backward looking.

In addition, this game theory takes into account the complex human interaction because humans act strategically. There are also many more important interactions: labor markets, credit markets, markets for information and goods of variable quality. Evolutionary game theory also approaches: modeling of chance, differential replication, out of equilibrium dynamics, and population structure.

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 because social outcomes are often influenced by recent past. Society cannot be well-modeled by a single game, especially one with an unchanging structure. Overall, game theory has a narrow scope of institutions. In reality, games overlap and intersect because people participate in a variety of social interaction. This is important because players learn through the structure of the game, which results in cultural evolution. This then affects how the players play the game and how they play other games that they are involved in. People also update their behaviors according to change and local information. Moreover, some characteristics of Evolutionary modeling includes: 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 and among groups.

The Hawk Dove Game is commonly applied to culturally or genetically transmitted human behavioral traits such as aggression and sharing.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 inflicting costs on doves. Thus, both doves and hawks are better off with fewer hawks. However, the Nash equilibrium of p* = v/c, in which v is the prize to be divided and c is the cost of losing a fight seems to indicate more Hawks as a desirable outcome, which is a weak best response. Based on Hawk Dove Game, the average payoff is when p=0 when there are no hawks at all. Overall, if there is only one strategy to replicate, it should remained unchanged, however the population may be invaded by mutants. This game is typically used to explore the issues that arise in regards to ownership and division of resources.

John Maynard Smith (1974), who is a biologist proposed the solution to the Hawk Dove Game, which was to find a way to reduce the number of interactions between hawk and doves that results in conflict. He suggested that “if owner plays Hawk, if intruder play Dove” labeled “Bourgeois”, where everyone's territory is made prevalent. In other words, proprietorship is never in question and everyone has an equal probability of being an owner.

Example: When Bourgeois meets a Hawk, half of the time it is not the owner and it then acts like a Dove, thus avoiding a fight. The other half of the time, the Bourgeois is an owner and they fight, but with the probability of winning as 1/2, the expected pay off would be (v-c)/4.

Overall, Bowel's points out the the key success of a Bourgeois is the use of additional information to create asymmetry among players.

Problems that arise from Smith's solution:

(a.)Ambiguity of possession arise

(b.)Private property rights could have evolved spontaneously

(c.)Institutional crowding out

(d.)Invisible hand arguments are misleading when applied to institutions and behavioral traits

A similar analogy to this game theory involves a "chicken" in which drivers never swerve, so when they meet, they crash. But, when the drivers meet the chicken, the chicken swerves and they both benefit.

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(a.) The domain: exogenous versus endogenous preferences and institutions

Bowels argues that many behaviors are best explained by social preferences: “in choosing to act, individuals commonly take account not only of the consequences of their actions for themselves but for others as well” (p.96). In other words, people not only care about the consequences of their action, but also about the intentions of others. An important aspect of social preferences is reciprocity, which is essentially people treat others according to the way the person behaves towards them or others. For example, people are generous to those behave well and people punish those who behave poorly. People act according to this reciprocity motives despite the fact that there are no incentives and costs. Other social preferences considered by Bowels includes: inequality aversion, envy and altruism.

In contrast, F.Y. Edgeworth, who is a founder of the neoclassical paradigm assumes self-interest and self-regarding preferences defined over outcomes. In the conventional approach, it is generally assumed that people act out of self-interest, while viewing that the other person is also acting out of self-interest. In addition, individuals act accoridng to social rules and norms with our limited cognitive resource. This contrast with conventional view “in which behavior is the result of often quite demanding individual cognitive processes addressing both evaluative and causal issues. This conventional individual cognition-centered view excludes behavior based on visceral reactions such as fear, disgust and much more, habit or evolved rules of thumb. It also presumes that people are able to predict what others will do and about the way the world works.

Bowels emphasizes that preferences are situationally specific and endogenous: "because endogenous preferences involve learning or genetic changes, behavior in the same situation changes over time” (p.97). Moreover, people evaluate outcomes through certain perspectives in regards to the current state or the current state experienced by a member of the group. Next, social institutions influence social interactions through the people we meet and the things we do, thus motivations are guided by culture.

On the other hand, conventional approaches generally view preferences as unchanging and that individuals seek to maximize their utility, which Bowels think limits economists view of both behavior and social evaluation. Conventional approaches seems to ignore other behavior aspects such as the fact that things change and the situation.

One of the conventional approach models individual behaviors through utility function:

U= U(x,y,z), which describes a list of of goods consumed by individuals.

The utility function is organized by the relationship between preference and indifference. The ordering of this function is also transitive and time invariant. For example, when prices change exogenously, individuals act accordingly, which is a form of beng rational. Hence, those who act outside of the order are considered irrational. The conventional model does take into account risks and uncertainty in which individuals are assumed to maximize their expected utility.

Although the conventional model of utility function take into account behavior, but it does not match recent empirical research about behavior. Bowels points out that the indifferent aspect in the conventional approach ignores the idea that changes in taste occurs. For example, individuals may not like one thing at first, but they may grow to like it or become accustomed to it. In other words, preferences may adjust to certain situations. According to the discounted utility model, you would continue to be indifferent towards that good, which is also called stationarity property:

U( y+x) - U(y) = {(U(y+x') - u(y)dn (change this p.105).

Daniel Kahneman, amost Tversky, Richard Thaler and their co-authors suggested prospect theory that takes into account four aspects that the conventional paradigm does not which are: people don’t evaluate risky decisions based on expected utility, framing (situations often frame choices), experienced hedonic utility, and framework that behaviors are situation-dependence. If the utility function was to explain actual behavior, it should argue that changes in states or events rather than states.

Bowels suggest that social preferences are these other regarding and processing regarding reasons for behavior (e.g. people hate being taken advantage of, people care about others as opposed to maximizing utility).

Process-regarding preference: individuals' evaluation of the state depends on the condition on how it came about rather than the intrinsic characteristics of the state. (e.g. the desire to help the homeless/poor as a result of bad luck not because they were lazy)

Other-regarding preference: individuals' evaluation of the state depends on how it is experienced by others which may include: spite, altruism, and caring about the relationship among the outcomes for oneself and others. (e.g. the desire to punish those who has done harm to you)

Table 3.1 (p.110).

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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

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

Efficiency Wage Theory

Background: When wage is above equilibrium level then you have unemployment due to the fact that firms are offering fewer jobs at that higher wage level. Because of this more workers want to get jobs at that higher wage level and when workers seek jobs and can’t find them, it leads to unemployment

Ways to get the wage above equilibrium level

Government requirement that firms pay a minimum wage above equilibrium level

Workers organize into labor unions and demand a wage above equilibrium level Definition of Efficiency wages

A wage that firms voluntarily choose to pay in order to increase profits

Idea of this is that a wage has 2 effects

it determines quantity of labor that’s traded in the market

wages influence the quality of labor that a firm hires

When a firm pays a higher wage it will get a higher quality of labor that makes it profitable for the firm to pay a wage above equilibrium level that can increase a firms profits

Reasons why firms would choose to pay a higher wage above equilibrium level

Wage may influence quality of labor that the firm hires

To give its workers a good deal

you don’t want to lose a job with a good deal

Ex: Henry Ford did this and paid his workforce a minimum of five dollars for an 8hr day, he shortened the workday and more than doubled the hourly rate of pay for a majority of his employees

He had many people coming to him looking for employment

Profits rose and output per hour of production labor increases

This is inconsistent with the Walrasian view that profit maximization entails paying one’s employees a wage equal to their supply price

Efficiency wage based on motivation, more productive worker

A happy, healthy worker is more productive

A firm that gives its workers more money than they can earn at another job leads to a happier, healthier worker

At higher wages, a company attracts a more skilled workers

In the Walrasian model, the employer is constrained by the workers’ labor supply decision and as a result the employer provides workplace amenities to lower costs of labor

A worker-friendly job will attract prospective employees at lower wages

The workers labor supply decision is the worker’s own utility, the employer will maximize profits by evaluating the importance of workplace amenities

This result does not hold when the effort is noncontractible

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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>.