Inequity aversion. Puzzles from experiments

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Alvin Phillips
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1 Inequty averson Readngs: Fehr and Schmdt (1999) Camerer (2003), Ch. 2.8, pp Sobel (2005) pp Puzzles from experments Compared to self-nterest model: Too much generosty & cooperaton Dctator games, publc good games Ultmatum games (genune or strategc generosty?) Trust games (trust or generosty?) Too much sanctonng Ultmatum games, publc good games Too condtonal on others behavor Ultmatum, publc good, and trust games Too context dependent Dctator games: effects of non-anonymty, recpent s dentty, ext opton, take opton Valdty Strange thngs happen n labs. So what? Internal valdty: Replcablty Wll others get the same result? Was the experment conducted professonally? External valdty: Wll smlar results occur outsde the lab? What s smlar l between the lab and the outsde world? What s not? What matters of ths? Refer to exstng theores: Whch dfferences would we, theoretcally, expect to matter? E.g.: In the real world, stakes are hgher New experment: Hgher stakes! Hypotheses on ext. valdty mght be tested n the lab! ccumulated body of evdence, establshed regulartes: New theores 1

2 Proposed explanatons Inequty averson preference for equal payoffs Recprocty preference for repayng kndness wth kndness and meanness wth meanness ltrusm Carng for others payoff, or others utlty Preferences for socal approval Prefers to be lked by others ll these explanatons nvolve non-standard preferences (note: not rratonalty!). Explanatons: ad hoc vs. consstency nythng can be explaned by ad hoc adustments of preference assumptons! shares wth others, does not has a preference for sharng, does not? sanctons others, does not has a preference for sanctonng others, does not? Two approaches: 1. Stck to self-nterest t model, look kfor mechansms makng gvng or sanctonng ndvdually proftable Gvng socal status well-pad ob ncome Sanctonng reputaton as (rratonally) tough type better barganng poston hgher ncome Experments: Can control for such mechansms 2. dust preference assumptons, but requre General applcablty (consstent w. wde array of data) and/or: ased on knowledge from other dscplnes (psychology, anthropology, bology, neurology). Preferences for equty What f some ndvduals dslke nequty? Utlty: Increasng n own ncome and n equty Possble formalzaton (e.g.): 2 U u( x ) ( x x ) 0 Utlty ncreasng n own ncome, decreasng n absolute dstance between and s ncome (symmetrcal) Other possblty: Utlty depends on relatve relatonshp between own and others ncome (see olton and Ockenfels 2000) 2

3 Fehr and Schmdt (1999): model of nequty averson Indvduals care about own ncome, advantageous nequty, and dsadvantageous nequty Suffer more from dsadvantageous than advantageous nequty Smplfcaton: Lnearty t max Can alternatvely be wrtten: x x,0 maxx x,0 ( x x ) f x x ( x x ) f x x U (x x ) Fehr and Scmdt: Inequty averson max where, and β α, 0 β <1 x x,0 maxx x,0 45º lne s utlty as a functon of s ncome, for a gven x x ll else gven, prefers s ncome to equal hers; s utlty declnes n ther ncome dfference, more so f herself s worst off. x Ultmatum game: Inequty averse responder Responder,, prefers hgh payoff to hmself, and equalty between hmself and the proposer,. Choce: Reect: {x,x }={0,0} ccept: {x,x }={(1- s)x, sx} Offered share s = 0.5: ccept yelds same ncome dfference as reect. ccept yelds more ncome than reect. Offer s accepted. Offered share s >0.5: ccept: hgher ncome dfference than reect. ccept yelds more ncome. ssumpton β < 1: One wll never throw away ncome to avod advantageous nequalty. Offer s accepted. 3

4 Inequty averse responder (cont.) Offered share s <0.5: ccept: hgher ncome dfference than reect. ccept yelds more ncome. No upper boundary on α : We may throw away ncome to avod dsadvantageous nequalty. maxx x,0 maxx x,0 U ( accept) sx [(1 s) X sx ] sx [ X 2 sx] X[ s (12 s)] U ( reect ) 0 Reect s preferred f X[ s (1 2s)] 0.e. f s 1 2 Note: X doesn t matter! Example α = 2, β = 0.4 Offer from Proposer (): s = 0.2 max U x x,0 maxx x,0 ( accept) X 2max X X, max X X, 0 = 0.2X X = X ( ) = - X ( reect ) 0 U wll reect, regardless of the sze of the pe to be shared. Inequty averse Proposer Prefers hgh payoff to hmself () and equalty between hmself and the responder (). Offered share s = 0.5: If accepted: Yelds max. equalty, but less than max. ncome oth self-nterested and nequalty-averse responders wll accept s = 0.5 Offered share s >0.5: If accepted: Yelds less ncome than s = 0.5, and less equalty Proposer wll never offer s > 0.5 4

5 Inequty averse Proposer (cont.) Offered share s <0.5: If accepted: Lower s, hgher ncome, but less equalty Whch s most mportant? s utlty when s 0.5, gven that accepts: U x max x x,0 max x x,0 (1 s ) X [(1 s ) X sx ] X( s(2 1) 1 ) Ths s ncreasng n s whenever β > 0.5 If acceptance were not a concern (dctator game), would offer s = 0 f β < 0.5, s = 0.5 f β > 0.5, and be ndfferent between any offer s [0, 0.5] f β = 0.5. Strategc nteracton must take nto account: wll accept? ssume nequty averse preferences, common knowledge: α = α = 2, β = β = 0.4 Snce β < 0.5, would prefer to keep all of X hmself, despte hs nequty averson. However, wll reect f s Knowng ths, offers s = 0.4 (or: slghtly more). accepts. Self-nterested Proposer, nequty-averse Responder Let α = 0, β = 0, α = 2, β = 0.4 Common knowledge Responder wll reect f s < 0.4 Threat s credble, due to s nequty averson Knowng ths, Proposer wll offer 0.4 No dfference between the behavor of selfnterested and nequty-averse Proposers! 5

6 If Proposer does not know Responder s type must consder the probablty that s nequty-averse. If possble (n the lab, t s usually not!), a self-nterested would pretend beng nequty-averse. In some stuatons, the exstence of nequty-averse types makes self-nterested types behave as f they were nequty-averse too. Competton Responder or proposer competton: Observed outcomes usually very nequtable 1 person reaps (almost) all gans, others get (almost) nothng. Double aucton markets: Observed outcomes usually conform ncely to the self-nterest model Do such results contradct the assumpton that (at least some) players are nequty averse? n-person nequty averson Fehr-Schmdt model wth n ndvduals: Normalzes nequty averson by the number of others (otherwse every new player k would decrease s utlty unless x k = x ) Self-orented: compares hmself to everyone else, but does not care about nequalty between others Crucal queston: What s the relevant peer group? 1 U ( x ) x n 1 max n 1 1 x x,0 max x x,0 6

7 Proposer competton You re sellng a house wth market value X. If t s not sold, your gan s 0 (you re movng, no rental market). For any nterested buyers, ts value s X. Sales process: 1. Potental buyers gve sealed offers s X 2. You ether reect all offers (no sale), or you accept the offer you prefer most. If ndfferent, actual buyer s pcked randomly among those you thnk best. 3. Trade takes place accordng to accepted offer (f any). 4. If sale took place, your payoff s s h X (h s the buyer). uyer s gan s (1-s h )X. No sale: ll get payoff 0. If only 1 potental buyer: Standard ultmatum game. uyer: Proposer. Seller: Responder. (Sequence!) ssume: 10 potental buyers. Your β < 0.5, so you wll pck the hghest offer. Proposer competton cont. Self-nterest predcton: Several proposers offer s=1, whch s accepted When there are several potental buyers who all value the house at X, you wll get X. ssume: Every player s nequty-averse If buyer s s offers s reected, he wll experence unfavourable nequty: Hs payoff=0, someone else s>0 If hs offer s accepted, there wll be nequty anyway, but hs ncome wll ncrease, and the nequty can be turned to hs advantage The only (subgame perfect) Nash equlbrum s that at least two proposers offer s=1, of whch one s accepted. Why doesn t nequty averson affect outcome wth proposer competton? No sngle player can enforce an equtable outcome. Gven that there wll be nequalty anyway, each proposer has a strong ncentve to outbd hs compettors n order to turn part of the nequalty to hs advantage and to ncrease hs own monetary payoff. ff (Fehr and Schmdt 1999, p.834) No buyer can secure less dsadvantageous nequalty between hmself and the monopolst (you) by offerng you a relatvely low share: If he tres, you can ust pck someone else s offer. Thus, nequty averson becomes rrelevant. 7

8 Crtcsms of the Fehr-Schmdt model Lnearty Dctator games: Dctator wll gve ether 0 (f β < 0.5) or 0.5 (f β > 0.5) Possble modfcaton: Utlty concave n nequty Who s the reference group? Lab: ll subects n experment? Opponent(s)? Outsde lab...? Flaws and aggressve marketng? nmore and Shaked (JEO 2010) See Mcro data across games not consstent wth fxed ndvdual α s and β s (lanco, Engelmann, Normann 2011) Next tme: Recprocty preference to repay knd ntentons by knd actons, and mean ntentons by mean actons Readngs: Camerer, C. (2003), pp (Compendum; Ch can be skpped). Sobel, J. (2005). See also: Rabn, M. (1993), Fehr and Gächter (2002). 8

Problems to be discussed at the 5 th seminar Suggested solutions

Problems to be discussed at the 5 th seminar Suggested solutions ECON4260 Behavoral Economcs Problems to be dscussed at the 5 th semnar Suggested solutons Problem 1 a) Consder an ultmatum game n whch the proposer gets, ntally, 100 NOK. Assume that both the proposer