Abstract
This chapter presents the interpretation of “approval theory” using the image score model and reputation dynamics from evolutionary game theory. The image score model corresponds to the aspect of approval theory describing the dynamics between the general norm and approval behaviors in the practical domain given that all individual norms are identical and coincide with the general norm in the normative domain. Reputation dynamics describe the process in which the general norm is realized from multiple individual norms in the normative domain through the approval behaviors in the practical domain. Interpreting approval theory with the image score model reveals that the region of the general norm is determined depending on the fraction of a distinctive approver who makes a sympathetic approval if the owner’s property ownership is justified by the general norm and autonomously approves otherwise. Interpreting approval theory using reputation dynamics reveals the nature of the general norm, which is the giver of the “social state” selected from among many individual norms. Furthermore, the analysis reveals multiple general norms satisfying this property and shows that in some cases, the general norm adopted among individuals in a “social state” may differ. At the same time, the region of justification has locality in terms of mutual approval among individuals whose property ownership are not mutually justified.
Tetsuya Kawamura, “Kihan to Rigai ni kakawaru Shonin Riron no Kaishaku (Interpretation of the confirmation theory about the norms and the interests),” Keizai-Ronso (The Economic Review), vol. 183, no. 3 (July 2009), pp 73–86. Kyoto Daigaku Keizai Gakkai (Kyoto University Economic Society).
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Notes
- 1.
Here, the term “profit” is a concept including emotional interests based on the personality of each person (autonomous or synchronous in this chapter) and does not regulate only the payoff obtained from property ownership.
- 2.
The condition of this payoff matrix is indispensable for using the results of the two models described below. The discussion in this chapter can be applied only when the payoff matrix in the practical area is a prisoner’s dilemma satisfying this condition.
- 3.
This assumption is necessary for analyzing the region of the general norm. If this assumption is not satisfied, there is a possibility that the region of the general norm will not converge.
- 4.
Consider a case where a distinctive approver regards the owner’s property ownership as justified by the probability p in the beginning of the game. In the image score model, if p is treated as an object of evolution, any payoff matrices in the class of the prisoner’s dilemma dealt with this chapter will evolve to p = 1 regardless of distribution of approval method.
- 5.
How much this ratio departs from Si(Ii(Dip))/Si(Ii(Djq)) − 1 depends on how many times approvers mutually approve goods with the same counterpart in one generation.
- 6.
In Ohtsuki and Iwasa (2004), each player plays only one game with only one opponent, and the fitness is determined by the result of the game. In Ohtsuki and Iwasa (2006), each player plays a game with the same opponent only once; however, they re-match the opponent and play multiple games, and the fitness is determined by total profit in each generation. The difference between these two settings does not make a significant difference to the results.
- 7.
This way of transmitting the reputation is called indirect observation. In Leimar and Hammerstein (2001), all third players who do not participate in the game observe the behavior of the two players and directly observe the reputation of the two according to each reputation rule (direct observation). Unlike the indirect observation, in the direct observation, the reputation for a player of all the other players does not always coincide.
- 8.
As an evolutionary game strategy, it is possible to assume infinite strategies with input other than the opponent’s behavior. For example, Pablov strategy includes his own action in addition to the opponent’s action. However, the reputation rule in reputation dynamics cannot be regarded as input of the action rule, which is a strategy. Action rules assign actions based on their reputation, but their reputation is determined based on the reputation rules of the third players who do not participate in the game. Therefore, each player has an action rule and reputation rule as a set, but his reputation rule cannot be an input of his action rule.
- 9.
Because the combination of any pair of “leading eight” is also an ESS, such invasion of pairs is temporary; however, the ratio of the eight norms will change after the invasion.
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Kawamura, T. (2020). Interpretation of Approval Theory Related to Norms and Interests: Interpretation by Image Score Model and Reputation Dynamics. In: Yagi, K. (eds) From Reproduction to Evolutionary Governance. Evolutionary Economics and Social Complexity Science, vol 20. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54998-7_7
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