A Theory of Fairness, Competition, and Cooperation
1998 · paper · Economics
Proposes a model in which some people care about equity, to explain why people exploit bargaining power in competitive markets but not bilateral bargaining, and sustain cooperation through costly punishment. The environment determines whether fair or selfish types dominate behavior.
Checked: PDF from web.stanford.edu, fetched 5 Oct 2026. Page numbers are those of that PDF.
12 findings
Substance Section IX summary says "Likewise, in a simultaneous public good game with punishment, even a small minority of selfish players can trigger the unraveling of cooperation", but the unraveling result (Prop. 4) is for the game without punishment.
- p. 40 Section IX, second paragraph
in a simultaneous public good game with punishment, even a small minority of selfish players can trigger the unraveling of cooperation
- p. 40 Section IX Summary, 2nd paragraph
Likewise, in a simultaneous public good game with punishment, even a small minority of selfish players can trigger the unraveling of cooperation.
- p. 40 Section IX, next sentences
a minority of fair-minded players can force a big majority of selfish players to cooperate fully in the public good game with punish-
Judge's note: Checked p.40 image: the text reads 'with punishment'. Proposition 4 (p.23–24) is introduced as the one-stage public good game, i.e. without punishment, and its part (b) gives the unraveling result. Proposition 5 (p.25) shows that one or a few enforcers can sustain full cooperation in the game with punishment, and the next sentence of the summary says exactly that. The sentence attributes the result to the wrong game.
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Reference or label The text cites "Güth and Tietz [1990]" (pp. 2 and 10), but the only 1990 Güth entry in the reference list is "Güth, Werner, Rolf Schmittberger, and Reinhard Tietz" (Journal of Economic Psychology, XI (1990)).
- p. 2 Introduction
[Güth and Tietz, 1990;
- p. 10 Section III.A
Güth and Tietz [1990]
- p. 51 References
Güth, Werner, Rolf Schmittberger, and Reinhard Tietz
- p. 10 Section III.A
Gu¨ th and Tietz [1990]
Only the authors can say what is right here.
Judge's note: On p. 10 the crop shows 'Güth and Tietz [1990]'. A text search finds the same two-author form on p. 2. The p. 51 reference list has a single 1990 Güth entry, and it lists three authors. The author list in the citations and in the reference entry disagree, and only the authors can say which is right.
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Reference or label Forsythe, Horowitz, Savin, and Sefton are cited as [1994] (p. 847 text; Table I 'FHSS [1994]'), but the reference list gives "Games and Economic Behavior, VI (1988), 347–369".
- p. 31 Section VI
Horowitz, Savin, and Sefton [1994]
- p. 11 Table I
FHSS [1994]
- p. 50 References
Games and Economic Behavior, VI (1988), 347–
- p. 31 Section VI
Forsythe, Horowitz, Savin, and Sefton [1994]
Judge's note: Checked on the images: text p. 847 says 1994 and the reference on p. 866 says 1988. This is the only Forsythe entry. The year mismatch is internal and verifiable. That 1994 is the correct year (GEB vol. VI) rests on outside knowledge, but the in-text year is used consistently twice.
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Reference or label p. 846: "As discussed in Section V, this equilibrium is a natural focal point". The sentence is itself in Section V, and the focal-point argument is in Section IV (p. 842).
- p. 30 Section V, first paragraph
As discussed in Section V, this equilibrium is a natural focal point.
- p. 26 Section IV, first paragraph
Hence, this equilibrium is a natural focal point that serves as a coordination device
- p. 30 Section V, public good game with punishment paragraph
As discussed in Section V, this equilibrium is a natural
- p. 26 Section IV, after Proposition 5
Hence, this equilibrium is a natural focal point that
Judge's note: Section V ('Predictions across Games') starts on PDF p. 27 (main.txt line 1774). The sentence is on PDF p. 30, inside Section V. The focal-point/refinement argument ('Hence, this equilibrium is a natural focal point that serves as a coordination device') is on PDF p. 26 (p. 842), in Section IV. Section V has no earlier discussion of it.
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Reference or label Fehr, Gächter, and Kirchsteiger are cited as 1997 (pp. 848–849), but the reference list gives "Econometrica, LXV, No. 4, (1996), 833–860".
- p. 32 Section VI
Fehr, Gächter, and Kirchsteiger 1997
- p. 33 Section VI
Gächter, and Kirchsteiger [1997]
- p. 50 References
Econometrica, LXV, No. 4, (1996), 833–860.
- p. 33 Section VI
Fehr, Ga¨chter, and Kirchsteiger [1997]
Judge's note: The text gives 1997 twice (main.txt lines 2163 and 2173). The reference on p. 866 (image checked) says 1996, and it is the only FGK entry. The mismatch is internal. That Econometrica vol. LXV is 1997 rests on outside knowledge.
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Reference or label Andreoni and Miller are cited as [1995] (pp. 848 and 852), but the only reference entry is "SSRI Working Paper, University of Wisconsin, Madison, 1996."
- p. 32 Section VI
In the study by Andreoni and Miller [1995]
- p. 36 Section VIII
Andreoni and Miller [1995] is based on the assumption of altruistic motives.
- p. 49 References
SSRI Working Paper, University of Wisconsin, Madison, 1996.
- p. 36 Section VIII
Andreoni and Miller [1995] is based on the assumption of altruistic motives
Judge's note: Images checked: p. 848 text gives 'Andreoni and Miller [1995]' and the reference on p. 865 says 1996. Section VIII (line 2398) also says 1995. There is no 1995 entry. Which year is intended is for the authors to say, but the citation does not match the list.
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Reference or label Kachelmeier and Shehata reference gives the journal as "Journal of Economic Organization and Behavior, XIX (1992), 145–168"; the same list names it "Journal of Economic Behavior and Organization" for Güth et al. (1982).
- p. 51 References
Journal of Economic Organization and Behavior, XIX (1992)
- p. 51 References, Güth et al. 1982
Journal of Economic Behavior and Organization, III (1982)
- p. 51 References, Güth et al. 1982
Journal of Economic Behavior and Organization
- p. 51 References
Journal of Economic Organization and Behavior, XIX (1992), 145–168.
Judge's note: Both entries are on PDF p. 51. The Kachelmeier–Shehata entry reverses 'Behavior' and 'Organization', while the Güth, Schmittberger and Schwarze entry gives 'Journal of Economic Behavior and Organization'. The reference list itself shows the inconsistency, so the fix is clear.
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Reference or label Slonim and Roth reference reads "Econometrica, LXVI (1997), 569–596"; the volume and the year appear not to match.
- p. 52 References
Econometrica, LXVI (1997), 569–596.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: Econometrica volume LXVI (66) is the 1998 volume, and Slonim and Roth's article appeared in 1998, 66(3), 569–596. The page image (PDF p. 52) shows LXVI with 1997, and the text cites the work as 'Slonim and Roth [1997]' (lines 479–480, 660–661, 669–670 of the extract). The files cannot show whether the year or the volume is the error, so this goes to the authors.
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Wording The proof of Proposition 1 says the acceptance probability F(s/(1 − 2s)) "is equal to one if s ≥ ᾱ(1 + 2ᾱ)"; the threshold that makes the step work is ᾱ/(1 + 2ᾱ) = s'(ᾱ).
- p. 12 Proof of Proposition 1, last sentences
which is equal to one if s ≥ ᾱ(1 + 2ᾱ)
- p. 12 Proof of Proposition 1, last paragraph
if s ≥ ᾱ(1 + 2ᾱ)
Only the authors can say what is right here.
Judge's note: My working: a responder with type α accepts s < 0.5 iff s − α(1−2s) ≥ 0, iff α ≤ s/(1−2s). So the acceptance probability is F(s/(1−2s)), which equals 1 iff s/(1−2s) ≥ ᾱ, iff s ≥ ᾱ/(1+2ᾱ). The page image and the text layer ('a (1 1 2a )', with no slash, while the next bound keeps its '/') both show the product form. As printed the condition is sufficient but not tight: for ᾱ = 1 it gives 3 instead of 1/3, which makes it vacuous. The conclusion s ∈ (s'(α̲), s'(ᾱ)] needs the quotient. Proposition 1 as stated (eqs. 4–5) stands.
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Wording The proof of Proposition 1 says the acceptance probability is "equal to zero if s ≤ α̲/(1 + α̲)"; the correct bound is α̲/(1 + 2α̲) = s'(α̲).
- p. 12 Proof of Proposition 1
equal to zero if s ≤ α/(1 + α)
Only the authors can say what is right here.
Judge's note: The page image and the text layer ('a /(1 1 a )') show the denominator without the 2. My working: F(s/(1−2s)) = 0 iff s/(1−2s) ≤ α̲, iff s ≤ α̲/(1+2α̲). A checked counterexample shows the printed statement is false: take α uniform on [0.5, 1] and s = 0.3 ≤ 1/3. Then s/(1−2s) = 0.75 and F = 0.5, not 0. Eq. (4) uses the correct s'(α̲), so Proposition 1 stands; the slip is in the proof step only.
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Wording p. 845: "Except for the Isaac and Walker experiments with n = 10 a single player with a + βi < 1 is sufficient for the violation of the necessary condition for cooperation, k/(n − 1) < a/2". The Isaac–Walker n = 4, a = 0.75 treatment in Table II is also an exception.
- p. 29 Section V, public good paragraph
Except for the Isaac and Walker experiments with n = 10 a single player with a + βi < 1 is sufficient for the violation
- p. 22 Table II, Isaac and Walker rows
4and10 0.75
- p. 29 Section V, public good paragraph
Except for the Isaac and Walker experiments with n = 10 a single player with a + β_i < 1 is sufficient for the violation of the necessary condition for cooperation, k/(n − 1) < a/2.
- p. 29 Section V, public good paragraph
Except for the Isaac and Walker experiments with n = 10 a single player with a + βi < 1 is sufficient for the violation of the necessary condition for cooperation
Judge's note: Prop. 4(c) on p. 839 requires k/(n−1) < (a+βj−1)/(αj+βj) < a/2, so k/(n−1) < a/2 is a strict necessary condition. Table II lists Isaac and Walker [1988] with group size '4and10' at a = 0.3 and at a = 0.75. With k = 1, n = 4, a = 0.75: 1/3 < 0.375, so the condition is not violated. Every other non-Isaac–Walker row does violate it (n=5, a=0.5 gives equality, which violates the strict inequality). The stated exception set is therefore incomplete. The general argument is little affected.
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Wording Proof of Proposition 3 opens "We first show that s = 1, which is accepted by all responders, is indeed a subgame perfect equilibrium", but Proposition 3 and the proof's conclusion concern s = 0.
- p. 42 Appendix, Proof of Proposition 3, first sentence
We first show that s = 1, which is accepted by all responders, is indeed a subgame perfect equilibrium.
- p. 43 after (A10)
it is an equilibrium that the proposer offers s = 0 which is accepted by all responders
- p. 42 Proof of Proposition 3, first sentence
We first show that s = 1, which is accepted by all responders,
Only the authors can say what is right here.
Judge's note: Images p.42/43: the first sentence says s = 1. Proposition 3 (p.16) states that the proposer offers s = 0. In the proof, U1(s) = 1 − s − ... (A8), and (A9)–(A10) conclude 'the proposer offers s = 0 which is accepted by all responders'. Under the proof's own argument (offers above 0.5 are dominated, and dU1/ds < 0), s = 1 is not the equilibrium being shown. The announced claim is wrong as printed, but the stated result still holds.
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31 minor (typos and the like; most checked by the judge only)
Reference or label Footnote 17 cites "Fehr and Falk [forthcoming]", but the reference list gives "Fehr, Ernst and Armin Falk, ... Journal of Political Economy, CVII (1999), 106–134."
- p. 20 Footnote 17
Fehr and Falk [forthcoming]
- p. 50 References
Journal of Political Economy, CVII (1999), 106–134.
Judge's note: The p. 20 footnote and the p. 50 reference entry disagree on the publication status and year of the same work. The citation should read [1999].
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Reference or label Andreoni (1988) reference gives the volume as "Journal of Public Economics, XXXXVII (1988)", which is a nonstandard Roman numeral.
- p. 49 References, Andreoni 1988
XXXXVII (1988)
- p. 50 References, Blinder and Choi
Theories of Wage Stickness
- p. 50 References, Blount
Human Decision Proces-ess
- p. 49 References
Journal of Public Economics, XXXXVII (1988)
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the intended volume is 37 (XXXVII) rather than 47 (XLVII). The crop shows 'XXXXVII'. It is malformed either way, so the volume is ambiguous. The 'Stickness' and 'Proces-ess' quotes in this cluster are judged under C044 and C045.
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Wording The text says "only 3 percent are below a share of 0.2" of the offers in Table I, while the Table I aggregate row prints 3.8.
- p. 10 Section III.A
while only 3 percent are below a share of 0.2
- p. 11 Table I, aggregate row
3.8
- p. 10 Section III.A
only 3 percent are below a share of 0.2
- p. 10 Section III.A
while only 3 percent are
Judge's note: On p. 11, Table I's aggregate row prints 3.8, and the weighted mean of the per-study values over 875 observations reproduces it (3.85). The text on p. 10 gives 3 percent, which is a loose round-down of the table figure. The aggregate also mixes in the Slonim and Roth rows, which use a 0.25 cutoff (footnote d).
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Wording (A9)–(A10): dU1/ds "is smaller than 0 if and only if β1 ≤ (n − 1)/n"; at equality the derivative is 0, and Prop. 3 uses the strict β1 < (n − 1)/n.
- p. 43 Appendix, (A10)
β1 ≤ (n − 1)/n.
- p. 16 Proposition 3
Suppose that β1 < (n − 1)/n.
Only the authors can say what is right here.
Judge's note: Reworked (A9) from the p.43 image: dU1/ds = −1 + [2 + (n−2)]β1/(n−1) = −1 + nβ1/(n−1). This is < 0 iff β1 < (n−1)/n, and it equals 0 at β1 = (n−1)/n. The 'iff ≤' claim is false at the boundary. Proposition 3 (p.16) is stated with the strict inequality, so the result stands.
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Wording Footnote 21 refers to "the remaining 25 percent of individual choices", while the text and Table II give 73 percent choosing gi = 0 (complement 27 percent).
- p. 29 Footnote 21
may explain much of the remaining 25 percent of individual choices
- p. 29 Section V text
although 73 percent of individuals indeed choose gi = 0
- p. 29 Footnote 21
remaining 25 percent of individual choices
- p. 29 Main text, public good paragraph
although 73 percent of individuals indeed choose g_i = 0
Judge's note: Both numbers checked on the images: p. 845 text says '73 percent of individuals indeed choose gi = 0', the Table II total row gives 1042 subjects and 73, and footnote 21 says 'remaining 25 percent'. The complement is 27. The 25 may be a loose approximation, so this is minor.
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Wording The Figure II caption reads "Distribution of Contributions in the Final Period of the Public Good Game with Punishment", but the legend plots both 'with punishm.' and 'without punishm.' series.
- p. 23 Figure II caption
Distribution of Contributions in the Final Period of the Public Good Game with Punishment
Judge's note: The p. 23 crop shows two legend series while the caption names only the punishment condition. The caption is incomplete, but the data shown are clear from the legend.
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Wording Footnote 25: "A defector who imposes a punishment of one on a cooperator gains [−βi/(n − 1)](1 − c) > 0 in nonpecuniary terms and has material costs of c. Thus, he is willing to punish if |βi| ≥ [c/(1 − c)](n − 1) holds." This omits the effect of the cost c on the defector's comparisons with the other n − 2 players.
- p. 34 footnote 25
A defector who imposes a punishment of one on a cooperator gains [−βi/(n − 1)](1 − c) > 0 in nonpecuniary terms
Only the authors can say what is right here.
Judge's note: My own working under eq. (1) with βi < 0, for a defector ahead of all others: punishing one cooperator by 1 widens the gap to that cooperator by (1−c), a gain of |β|(1−c)/(n−1). It also narrows his lead over each of the other n−2 players by c, a loss of |β|c(n−2)/(n−1). Against players he is level with or behind, the loss is αc/(n−1). The net is |β|[(1−c) − c(n−2)]/(n−1) − c. Counterexample: n=4, c=0.2, |β|=0.75 meets the footnote's threshold, but the net is 0.1 − 0.2 < 0. The printed 'willing to punish if' condition is therefore not sufficient for n > 2. The true threshold is higher, so the footnote's qualitative conclusion ('only implausibly high |β|') stands.
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Wording p. 853: "disadvantages of Rabin's model are that ... it gives predictions if it is applied to the normal form of important sequential move games". A qualifier (e.g., 'implausible') appears to be missing.
- p. 37 Section VIII
it gives predictions if it is applied to the normal form of important sequential move games
- p. 37 Section VIII
it gives predictions if it is applied to the normal form
Judge's note: Page image checked. The sentence lists disadvantages, and footnote 30 explains that the predictions are counterfactual (unconditional cooperation by the second mover). As printed, 'gives predictions' does not describe a disadvantage.
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Wording Proof of Prop. 4(b): (A16) step 'U_l(0) − (1−a)g_l + β_l (n−2(k+1)+1)/(n−1) g_l < U_l(0) − (1−a)g_l + (n−2k−1)/(n−1) g_l' uses β_l < 1 but holds only if n−2k−1 > 0; also '0 = g1 = . . . gk' lacks an '='.
- p. 45 Appendix, proof of Prop. 4(b)
0 = g1 = . . . gk
- p. 45 (A16), third line
< U_l(0) − (1 − a)g_l + (n − 2k − 1)/(n − 1) g_l
Only the authors can say what is right here.
Judge's note: From the p.45 image: the chain is printed '0 = g_1 = . . . g_k' (S4 typo). In (A16), n−2(k+1)+1 = n−2k−1, and replacing β_l by 1 gives a strict decrease only when that coefficient is positive. Counterexample within part (b)'s assumptions: n=4, k=2 (k/(n−1)=2/3 > a/2 for any a<1), β_l=0.5. Then β_l(n−2k−1)/(n−1) = −0.167, which is not < −0.333. The result survives: when n−2k−1 ≤ 0, U_l(g_l) ≤ U_l(0) − (1−a)g_l < U_l(0) directly. So the step is faulty but the proposition stands.
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Wording Proof of Prop. 4(c): intermediate line "= y − g − (n − k)ag − α_j/(n−1) kg" has the wrong sign on (n−k)ag.
- p. 46 Appendix, proof of Prop. 4(c), derivation of U_j(g−Δ)
= y − g − (n − k)ag −
Only the authors can say what is right here.
Judge's note: p.46 image: the first line has +(n−k)ag, and (A19) has U_j(g) = y − g + (n−k)ag − ..., but the middle line prints −(n−k)ag. Collecting the Δ-free terms of the first line gives y − g + (n−k)ag − α_j k g/(n−1) = U_j(g), which the next line uses correctly. The slip is confined to one line, and (A20) is unaffected.
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Wording (A22): the chain 'x_j = y − g + a[...] − c(g−g_i)/(n'−c) − ((n'−c)/(n'−c))(g_i − g_i) = y − g_j + a[...] − (n' − c + c)(g−g_i)/(n'−c) = x_i' does not hold as printed.
- p. 47 Appendix, Proof of Proposition 5, eq. (A22)
(g_i − g_i)
- p. 47 eq. (A22) second line
= y − g_j + a[(n − 1)g + g_i] − (n' − c + c)
Only the authors can say what is right here.
Judge's note: p.47 image: the added term is (g_i − g_i), which is identically 0, and the second line starts with y − g_j where enforcer j contributes g. As printed, the second line equals x_i − (g − g_i), not x_j. Numeric check with n=4, n'=1, c=0.2, a=0.4, y=10, g=10, g_i=0: x_j = x_i = 9.5, but the printed second line gives −0.5. The intended rewriting uses (g − g_i) and y − g_i. The identity x_j = x_i itself is correct.
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Wording Appendix: "We mentioned already that the empirical evidence suggests that these parameters are positively correlated" has no earlier counterpart in the text.
- p. 48 Appendix, computation of probability
We mentioned already that the empirical evidence suggests that these parameters are positively correlated.
Only the authors can say what is right here.
Judge's note: I searched the full text for 'correlat', 'positiv' and 'Loewenstein'. The only earlier uses of correlation concern wages and effort, and the cross-situation correlation of behaviour (p.31). The Table III discussion (pp.27–29) treats the α and β distributions separately. No earlier statement says α_i and β_i are positively correlated, so the back-reference points to nothing in the paper.
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Typo The co-author is spelled "Agell and Lundborg 1995" in the text on pp. 1 and 5, but "Agell, Jonas, and Per Lundberg" in the reference list on p. 49.
- p. 1 Introduction
Agell and Lundborg 1995
- p. 5 Section II
Agell and Lundborg [1995]
- p. 49 References
Agell, Jonas, and Per Lundberg
Judge's note: Both spellings are visible in the crops (p. 1 citation list, p. 5 'Agell and Lundborg [1995]', p. 49 reference entry). This is an internal inconsistency in the same work's author name. Deciding which spelling is correct rests on outside knowledge (the author's actual surname); the text uses Lundborg twice.
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Typo Footnote 1 cites "Skinner and Slemroad [1985]", but the reference list has "Skinner, Jonathan, and Joel Slemrod".
- p. 2 Footnote 1
Skinner and Slemroad [1985]
- p. 52 References
Skinner, Jonathan, and Joel Slemrod
Judge's note: Footnote 1 on p. 2 reads 'Slemroad'. The reference entry on p. 52 reads 'Slemrod'. It is a misspelling in the citation.
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Typo Footnote 16 cites "Kahnemann, Knetsch, and Thaler [1986]"; elsewhere the text and Table I spell the name "Kahneman".
- p. 19 Footnote 16
Kahnemann, Knetsch, and Thaler [1986]
- p. 2 fn 1
Skinner and Slemroad [1985]
Judge's note: The p. 19 crop shows 'Kahnemann'. Page 1 and Table I on p. 11 read 'Kahneman'. The Slemroad part of this cluster is the same defect as C002 and is judged there.
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Typo "The rest of the paper is organized as followed." should read "as follows".
- p. 4 Introduction, outline paragraph
The rest of the paper is organized as followed.
- p. 4 Introduction
organized as followed
Judge's note: The crop of p. 4 shows 'organized as followed.' This is a grammatical slip.
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Typo Equation numbering jumps from (5) on p. 11 to (8) in Proposition 3 on p. 16; there are no equations (6) or (7).
- p. 11 Eq. (5)
(5)
- p. 16 Proposition 3, eq. (8)
(8)
Judge's note: In the layout text, the labels run (1), (2), (3), (4), (5), (8), (9), (10), ... and no (6) or (7) appears anywhere. The page images for pp. 13–15 show no displayed numbered equations. This is a cosmetic numbering gap.
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Typo Table I capitalises the payment method inconsistently: "(All Ss Paid)" for Cameron's first row and "(All Ss paid)" for Hoffman's first row, against "(all Ss paid)" in the other rows.
- p. 11 Table I, Study column
(All Ss Paid)
Judge's note: Confirmed on the p. 11 table image. This is cosmetic.
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Typo "proposer i can strictly increase this monetary payoff" should read "his monetary payoff".
- p. 13 Section III.B
proposer i can strictly increase this monetary payoff
Judge's note: The p. 13 crop shows 'increase this monetary payoff'. The phrase refers to proposer i's own payoff. This is a one-letter typo.
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Typo "If there are n players altogether, than giving away one dollar..." should read "then".
- p. 17 Section III.C, first line
players altogether, than giving away one dollar
Judge's note: The p. 17 crop shows 'players altogether, than giving away', continuing a conditional that begins on p. 16 with 'If there are n'.
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Typo p. 840 (PDF p. 24): "nonpecuinary benefit of at most βi dollars" is a misspelling of "nonpecuniary".
- p. 24 Section IV, after Prop. 4
nonpecuinary benefit of at most
Judge's note: The text layer (main.txt line 1551) reads "nonpecuinary". The paper's other instances (lines 1036, 2309, 3554, 3559, 3602) are spelled "nonpecuniary". On the page image the word is consistent with the misspelling, although the resolution is low.
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Typo p. 847: "our very simple model of linear inequality aversion is consistent, with the most important facts" has a stray comma.
- p. 31 Section VI, first sentence
model of linear inequality aversion is consistent, with the most
Judge's note: The comma is visible on the page image. It splits 'consistent with'.
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Typo Footnote 28: "optimistic beliefs about other subjects inequity aversion our model is consistent" is missing the possessive apostrophe (subjects') and a comma before 'our model'.
- p. 36 Footnote 28
about other subjects inequity aversion our model
Judge's note: The phrase is visible as quoted in the crop of footnote 28.
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Typo Proof of Prop. 4(b): "Player 1’s utility is given by" and "the utility player 1 gets if he deviates" should refer to player l.
- p. 45 Appendix, proof of Prop. 4(b)
Player 1’s utility is given by
- p. 45 below (A15)
where U_l(0) is the utility player 1 gets if he deviates
Judge's note: In the p.45 image and the text layer, the prose has the digit 1, while (A15) is written in terms of U_l, g_l and β_l for player l, the smallest positive contributor. Player 1 contributes 0 in this proof.
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Typo Proof of Prop. 5: "nonpecuniary loss of β1ε by creating inequality" should be β_iε, since the deviating enforcer is player i.
- p. 48 Appendix, proof of Prop. 5
nonpecuniary loss of β1ε by creating inequality
Judge's note: p.48 image shows the subscript 1. The same paragraph refers to player i and to 'Since 1 − a < β_i'.
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Typo Doubled closing parenthesis in "(roughly33)) c = 0.2".
- p. 48 Appendix, computation of probability
(roughly33)) c = 0.2
Judge's note: The p.48 image shows one opening and two closing parentheses around 'roughly' and footnote 33.
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Typo Blinder and Choi reference: "Theories of Wage Stickness" should be "Stickiness".
- p. 50 References
Theories of Wage Stickness
Judge's note: The p.50 crop shows 'Stickness,'. This is a misspelling.
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Typo Blount (1995) reference: journal name printed "Human Decision Proces-/ess" (= 'Procesess') instead of 'Processes'.
- p. 50 References, Blount 1995
Organizational Behavior and Human Decision Proces- ess
- p. 50 References, Blount
Human Decision Proces-
Judge's note: The p.50 crop shows 'Proces-' at the line end followed by 'ess,' on the next line. Joined, this reads 'Procesess', a misspelling of 'Processes'.
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Typo Blinder and Choi reference title reads "A Shred of Evidence on Theories of Wage Stickness"; 'Stickness' should be 'Stickiness'.
- p. 50
Wage Stickness,’’ Quarterly Journal of Economics
Judge's note: The page image (p. 866 of the journal, PDF p. 50) shows 'Stickness,' in the Blinder and Choi entry. 'Stickness' is not an English word, and 'wage stickiness' is the usual term, so this is a misspelling.
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Typo Stray commas in references: "On Expectations and Monetary, Stakes in Ultimatum Games" (Hoffman et al.), "Watabe, M., S. Terai, N., Hayashi" and "Roth, Alvin, E., and Ido Erev".
- p. 51 References, Hoffman et al.
Monetary, Stakes in Ultimatum Games
- p. 52 References, Watabe et al.
S. Terai, N., Hayashi
- p. 52 References, Roth and Erev
Roth, Alvin, E., and Ido Erev
Judge's note: All three are visible on the page images. In Hoffman et al. (PDF p. 51) a comma splits 'Monetary, Stakes'. In Watabe et al. (p. 52) the comma comes after 'N.' instead of between 'Terai' and 'N.', giving 'S. Terai, N., Hayashi'. Roth and Erev (p. 52) has 'Roth, Alvin, E.', while the entries on either side give 'Roth, Alvin E.' These are punctuation slips.
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Typo Rehder reference title opens with a double quotation mark and closes with a single one: "Japanese Transplants: After the Honeymoon,’ Business Horizons".
- p. 52 References
After the Honeymoon,’ Business Horizons
Judge's note: Everywhere else the text layer writes closing double quotes as two characters (’’), but here it has only one (’), which points to a single closing glyph in the PDF. At the resolution of the crop and the full page image I cannot clearly tell the closing mark apart from a double quote. Cosmetic either way.
Second check: none (judge only)