Reference groups and variable risk strategies

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Abstract

The present article examines two important effects that have been given scant attention in prior studies of variable risk strategies. The first effect, reference group sensitivity, is the degree to which decision makers’ aspirations are sensitive to their reference group. In this paper we compare the performances of decision makers with alternative levels of reference group sensitivity. Second, we introduce the novel concept of community effect. This relates to mobility among multiple segregated reference groups. The performance of decision makers residing in a world with one single population is compared with that of decision makers who have the possibility, which is more or less costly, to switch between multiple populations. The results support the findings from previous studies that variable risk strategies are preferred over fixed risk. The study of a community of populations provides additional insights that both support and complement previous research.

Section snippets

The standard model

The present article extends the effects considered in the standard references for aspiration level research (Herriott et al., 1985, Levinthal and March, 1981, March, 1988, March, 1996, March and Shapira, 1987, March and Shapira, 1992). In particular, March (1988) model, in which a decision maker's risk preference is a function of current resources relative to an aspiration level, serves as a baseline model and is referred to as the standard model.

In statistical terminology the standard model is

The community model

Previous studies (Herriott et al., 1985, March and Shapira, 1987) have proposed an extension to the standard model in which the aspiration level of each risk taker may depend on the resources Wj,t accumulated by othersAi,t+1=αψWj,t+α(1ψ)Wi,t+(1α)Ai,t.The weight ψ, given to the wealth accumulated by others in the decision maker's own population j, is bounded in the closed interval (0,1). We refer to it here as reference group sensitivity because it tracks the wealth of other members of the

The simulation

The simulation in the present paper is similar to the approach taken in previous studies (Levinthal and March, 1981, March, 1988, March and Shapira, 1987); it differs in examining previously unexplored parameters. In the present study, alternative levels of four parameters are examined: (1) the rate of aspiration adjustment α (0.10, 0.50, 1.00); (2) the reference group sensitivity ψ (0.00, 0.10, 0.50, 1.00); (3) the switching cost δ (0.10, 0.50, 1.00); (4) the number of possible populations M

Results for one population

The first panel in Fig. 1 shows the relation between ruin rate and cumulated wealth for maximal reference group sensitivity (ψ = 1.00) and zero switching costs (δ = 0.00). In the case of zero switching costs, all population members in the community model will be located in one place. In this case, the only difference between the standard model and the community model is the sensitivity to the wealth of others. The results for the community model, shown in the first panel of Fig. 1, are averages for

Results for multiple populations

Positive switching costs (δ > 0) lead to segregation among members of multiple populations. Thus, panels two, three and four in Fig. 1 show the results for values of δ (0.10, 0.50, 1.00) that will give rise to multiple populations. The results for the community model shown in Fig. 1 (panels 2–4) are averages for ψ = 1.00, across aspiration levels and across the number of possible populations.

Panels two and three in Fig. 1 shows the relation between ruin rate and cumulated wealth for complete

Comparison of the reference group model and the standard model

The purpose of this comparison for a single population of decision makers is to understand why the reference group model results in both a lower ruin rate and a higher level of wealth accumulation for the population than the standard model. The following section considers the community model.

Discussion

The community model has not previously been discussed in the literature, and only a few studies have considered aspirations that track the average wealth of a reference group. Posch et al. (1999) and Weibull (2002) are relatively recent examples. Weibull demonstrates how to construct a model of adapting rules that lead to the replicator dynamics and considers the possibility that an aspiration level tracks the average wealth of others. This appears to be a very promising extension of previous

Conclusion

The model developed in the present study continues the trend towards greater emphasis on social interaction, relative comparisons, and the context of decision-making rather than seeing the individual as facing a fixed decision environment with absolute decision criteria. The main result of our model is that reference group comparisons generally provide a more important basis for variable risk strategies than the decision maker's own situation. As multiple populations were considered, the

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    The author wishes to thank the editor, an anonymous reviewer, Markus C. Becker, Henrich Greve, Tage Koed Madsen, James G. March, Nils Stieglitz, participants of the Academy of Management meetings, and the Strategic Organization Design (SOD) seminar at the University of Southern Denmark for stimulating and helpful comments.

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