Migration and intergroup conflict

Transcription

1 Econoics Letters 69 (000) locate/ econbase Migration and intergroup conflict Kjell Hausken* University of tavanger, chool of Econoics, Culture and ocial ciences, P.O. Box 557, Ullandhaug, N-409 tavanger, Norway Received 5 October 999; accepted 5 June 000 Abstract Two groups in conflict produce and appropriate internally generated consuable output in a two-stage gae assuing equal within-group sharing and endogenous group sizes. It is shown how agents leave groups with high productive efficiency and igrate to groups with high appropriative and defensive capabilities. 000 Elsevier cience.a. All rights reserved. Keywords: Within-group strategic choice; Allocation of endowent; Production; Appropriation; Free-riding; Between-group copetition; Group decisiveness; Intergroup igration JEL classification: C7; C73; 7; 74 If you can t beat the, join the. If you can t join the, beat the. What is the underlying principle by which agents decide to beat or join groups? This article answers the question allowing groups to differ w.r.t. productive efficiency, appropriative and defensive capability, allowing varying degrees of decisiveness in between-group copetition. Assuing intergroup igration, this article extends two-level conceptions within three fields. Agents often prefer to produce consuable output, but ay have several reasons not to do so. First, production is costly. econd, produced output ay be appropriated. Third, an agent ay prefer to appropriate rather than to produce. Fourth, the agents ay prefer to free-ride. These reasons are probleatized when agents are allowed to igrate between groups. *Tel.: ; fax: E-ail address: kjell.hausken@oks.his.no (K. Hausken). The first is collective rent seeking (Katz et al., 990; Baik and hogren, 995; Hausken, 995a,b, 998; Baik and Lee, 997; Lee, 995; Nitzan, 99a,b, 994). The second is the analysis of the ipact of product-arket copetition on anagerial slack (Hart, 983; Horn et al., 995; Tirole, 988; Vickers, 995; Winter, 97). The third involves conflict between actors (Grossan, 99; Grossan and Ki, 995; Hausken, 000; Hirshleifer, 995; Neary, 997; kaperdas, 99; kaperdas and yropoulos, 997; Usher, 99; Usher and Engineer, 987; Noh, 998) / 00/ $ see front atter 000 Elsevier cience.a. All rights reserved. PII: (00)0036-8

2 38 K. Hausken / Econoics Letters 69 (000) Consider two groups in copetition. Agent j in group i is endowed with an initial resource endowent ri which ay either not be allocated (free-riding, leisure), or ay be allocated wij to production and sij to appropriation and defense (appropriation for short), 0 # wij sij 5 r i, i 5,. Two groups with sizes n and n produce consuable output (products, goods, outcoes, prizes, benefits, rewards, payoffs) n n B Ow B O w, j v j5 v5 where B and B specify how efficiently output is produced. Applying the conventional ratio for (Tullock, 967) to deterine each group s and each agent s ability to appropriate output, agent j s payoff in group is n n n F O j5s j j P (s, ) 5 B O(r s ) B O (r s ), () G n j5 v5 j j n n F j v F O j5sj F Ov5sv j where is the set of all strategies by all agents in the two groups except agent j, is the between-group decisiveness which specifies between-group sharing, and F and F specify how effectively output is appropriated (and defended). Allocation into production leads to enlargeent of the size of the pie of output produced by the two groups, while allocation into appropriation increases the share of the pie accruing to each group. We analyze a two-stage gae, solve each agent s axiization proble and check when ij P ij(s ij, ). ri to avoid free-riding. In the first stage agents decide which group to belong to, dependent on which group gives the highest payoff, suitably taking into account how the agents allocate their endowents between production and appropriation in the second stage. In so doing, each agent takes all the other agents group ebership decisions as given. Acknowledging equivalent agents, axiizing the aggregate group payoff is equivalent to axiizing the individual payoff in a syetric equilibriu where each agent receives the sae payoff. In so doing, agent j takes suitably into account how the agents allocate their endowents between production and appropriation in the second stage. In the second stage the agents ake their choices siultaneously and independently, taking the group sizes n and n as given. Agent j in group takes the production versus appropriation allocation of the other agents in group as given, and also takes the production versus appropriation allocation wv versus sv of the agents in group as given. He then chooses sj to axiize his payoff. We first consider the second-stage decision. etting the derivative of j j j j P (s, ) in () w.r.t. s equal to zero gives n n j n n j j j5 j v5 v n n s n F j v j F O s FO s j5 v5 j5 j v5 v n FO s j5 j n n n FO s FO s j5 j v5 v P (s, ) FO s F O s ]]]] 5]] B O(r s ) B O (r s ) G [B ] 5 0. () It is straightforward to endogenize the within-group sharing rule and show that egalitarian sharing is an equilibriu. ee Noh (998) for a fuller treatent of within-group sharing rules.

3 K. Hausken / Econoics Letters 69 (000) In a syetric Nash equilibriu identical agents devote the sae aounts w 5 w and s 5 s to j j production and appropriation, respectively. () siplifies to (n s) FB (n s) FB ( )n s(n s) FB F(n s) (B B) 5 0. (3) Multiplying (3) by F (n s) /F (n s) and subtracting fro that version of (3) where the indices and are peruted, gives /() ] 5 ] ]], (4) /() F (B B) /() /() /() /() /() /() F (B B) /() /() /() /() /() s 5 ]]]]]], (5) n ( )B (F B F B ) s 5 ]]]]]], n ( )B (F B F B ) /() /() F B (B B) j /() /() /() /() /() /() F B (B B) v /() /() /() /() P* 5 ]]]], (6) n ( )(F B F B ) P* 5 ]]]]. n ( )(F B F B ) In the first stage, agent j chooses groups or to axiize his payoff. Agent j is indifferent w.r.t. group ebership when P* 5 P *. Applying (4), (6), and n n 5 N, gives j v /() n ()/ F / n B F /() B ()/() ] 5] ]] 5 ] ] 5 ] ] 5 ] ], (7) n F n B F B n F B ] 5 ] ], (8) n F B /() /() F B /() /() /() /() F B F B /() /() F B /() /() /() /() F B F B n 5 N, n 5 N, n(n rb B) s 5 ]]]]]]], (9) n ( )NB n(n rb B) s 5 ]]]]]]], n ( )NB

4 330 K. Hausken / Econoics Letters 69 (000) /() /() /() /() B B F B rb F B rb * j * v ]]]]] ]]] /() /() /() /() ( )N ( )(F B F B ) P 5 P 5 5. (0) Free-riding is avoided when P (s, ij ij ij i ). r, which gives /() /() F B (B B) /() /() /() /() /() /() F B (B B) /() /() /() /() ]]]]., () ()(F B F B ) ]]]]., ()(F B F B ) for fixed sized groups and n B]] B. ( ) ], () n n r B]] B. ( ) ] ], n r for intergroup igration. An agent in group prefers intergroup igration rather than fixed sized groups when (0) is larger than P* in (6), i.e. j F /() B /() n ] ],]. (3) F B n The result in (4) is well known in the literature (Hirshleifer, 99; Grossan and Ki, 995; kaperdas and yropoulos, 997). The results in (5) (3) are not known and can be sued up in nine points. () If two groups can agree on equivalently increasing B 5 B, the equilibriu ixture of allocation into production and appropriation reains unchanged, although their payoffs increase. () Increasing B in group causes higher productivity and payoffs in group, but causes considerably ore appropriation and even higher payoffs in group. (3) Equivalently increasing F5 F in the two groups does not alter the equilibriu and the payoffs. (4) Increasing F in group causes higher productivity and payoffs in group, and ore appropriation and lower payoffs in group. (5) Increasing decisiveness causes larger allocation to appropriation and lower payoffs. (6) The ratio of the payoffs in groups and is inversely proportional to the ratio n /n of the group sizes, proportional to F /F (in a anner approaching independence as increases), and inversely proportional to B /B (in a anner that approaches linear dependence as increases). (7) Allowing intergroup obility when B. B causes igration to group in a anner that becoes ore pronounced when increases, and oderately large (and equivalent) payoffs in the two groups. (8) Allowing intergroup obility when F. F causes igration to and ore production in group in a anner that becoes less pronounced when increases, very high appropriation in group, and higher payoffs. (9) Intergroup igration causes the ratio s /s of allocation into appropriation to be inversely proportional to F /F, inversely proportional to B /B when 0 #,, and proportional to B /B when.. The significance of the results lies in the non-trivial iplications of the odel for resource allocation (division of labor) for each agent, welfare between groups, intergroup igration, and

5 K. Hausken / Econoics Letters 69 (000) adjustent of group size. Central to the odel is the placeent of consuable output in a coon pool. This creates a benchark for individual and group behavior where property rights are deterined (Neary, 997) by each group s ability to appropriate fro the coon pool. eterining property rights by other factors, e.g. closeness to production or judicial criteria for ownership, and allowing appropriated output not to be 00% exploitable (Grossan and Ki, 995), suggest an opposite benchark where appropriation is absent. The forer benchark causes agents up to a point to beat rather than join the group with higher productive efficiency. A group ay cause oveent toward, without reaching, the latter benchark by increasing its appropriative capability, encouraging the other group to increase its productive efficiency, decreasing the between-group decisiveness, or forbidding eigration (iplies higher payoff to the other group). References Baik, K.H., Lee,., 997. Collective rent seeking with endogeneous group sizes. European Journal of Political Econoy 3, 30. Baik, K.H., hogren, J.F., 995. Copetitive-share group foration in rent-seeking contests. Public Choice 83, 3 6. Grossan, H.I., 99. A general equilibriu odel of insurrections. Aerican Econoic Review 8, 9 9. Grossan, H.I., Ki, M., 995. word and plowshares? A theory of the security of clais to property. Journal of Political Econoy 03 (6), Hart, O.., 983. The arket echanis as an incentive schee. Bell Journal of Econoics 74, Hausken, K., 995a. Intra-level and inter-level interaction. Rationality and ociety 7 (4), Hausken, K., 995b. The dynaics of within-group and between-group interaction. Journal of Matheatical Econoics 4 (7), Hausken, K., 998. Collective rent seeking and division of labor. European Journal of Political Econoy 4 (4), Hausken, K., 000. Cooperation and between-group copetition. Journal of Econoic Behavior and Organization 4 (3), Hirshleifer, J., 99. The paradox of power. Econoics and Politics 3, Hirshleifer, J., 995. Anarchy and its breakdown. Journal of Political Econoy 03 (), 6 5. Horn, H., Lang, H., Lundgren,., 995. Managerial effort incentives, X-inefficiency and international trade. European Econoic Review 39, Katz, E., Nitzan,., Rosenberg, J., 990. Rent seeking for pure public goods. Public Choice 65, Lee,., 995. Endogenous sharing rules in collective-group-rent-seeking. Public Choice 85, Neary, H.M., 997. Equilibriu structure in an econoic odel of conflict. Econoic Inquiry 35, Nitzan,., 99a. Rent seeking with non-identical sharing rules. Public Choice 7, Nitzan,., 99b. Collective rent dissipation. The Econoic Journal 0, Nitzan,., 994. Modelling rent-seeking contests. European Journal of Political Econoy 0, Noh,.J., 998. A general equilibriu odel of two group conflict with endogenous intra-group sharing rules. Public Choice 98, kaperdas,., 99. Cooperation, conflict, and power in the absence of property rights. Aerican Econoic Review 8, kaperdas,., yropoulos, C., 997. The distribution of incoe in the presence of appropriative activities. Econoica 64, 0 7. Tirole, J., 988. The Theory of Industrial Organization. MIT Press, Cabridge, MA. Tullock, G., 967. The welfare costs of tariffs, onopolies, and theft. Western Econoic Journal 5, 4 3. Usher,., 99. The Welfare Econoics of Markets, Voting and Predation. University of Michigan Press. Usher,., Engineer, M., 987. The distribution of incoe in a despotic society. Public Choice 54, Vickers, J., 995. Concepts of copetition. Oxford Econoic Papers 47, 3. Winter,., 97. atisficing, selection, and the innovating renant. Quarterly Journal of Econoics 85, 37 6.