Nullified equal loss property and equal division values

Commons’tragedy

Axiomatic study

Risky Bargaining

Nullified equal loss property and equal division values (Theory and Decision) A plea for an egalitarian principle Sylvain Ferrières CRESE, Univ. Franche-Comté, France & HHL, Leipzig, Germany

Spring 2017

References

Commons’tragedy

Axiomatic study

Risky Bargaining

References

Main idea of the talk

Emergence of a principle reconciling individual and social interests. Axiomatic study in the cooperative games’framework. Application to bargaining under risk. =⇒ understand a general principle through an axiomatic study and economic applications.

Commons’tragedy

Axiomatic study

Risky Bargaining

Summary

1

Softening the tragedy of the Commons

2

Axiomatic study of the Nullified equal loss property

3

Application to bargaining under risk

References

Commons’tragedy

Axiomatic study

Risky Bargaining

References

Model and issue

A model close to Funaki et al. (1999) Perfectly divisible CPR, no storage feasible Fixed community N: pure appropriation externalities Common marginal labor cost q > 0 − Vector of individual work efforts → x = (xi )i∈N of sum xN Per unit production function f : positive, striclty decreasing and concave on [0, x] null thereafter f (0) > q

Commons’tragedy

Axiomatic study

Risky Bargaining

Model and issue Social Optimum 0 < xc N = argmax ( xN (f (xN ) − q) ) < x Non-cooperative game (N, (R+ , ui )i∈N ) Prior to choosing their individual efforts, distribution of the − total production ϕi (→ x )f (xN ). − − ui (→ x ) = ϕi (→ x )f (xN ) − qxi − =⇒ Nash equilibrium → x ϕ?

References

Commons’tragedy

Axiomatic study

Risky Bargaining

Extreme allocations

To each according to his work Where we meet Hardin (1968): − 0 ϕi (→ x ) = xi =⇒ xc N < xN < x To each according to his needs Where one expects much from one’s neighbor: xN − ϕi (→ x)= =⇒ 0 ≤ xN1 < xc N n

References

Commons’tragedy

Axiomatic study

Risky Bargaining

Optimal internal tax Convex combination of the last two shares Consider − ϕi (→ x ) = λxN /n + (1 − λ)xi then we recover a similar result by Sen (1966): ∃!λ? ∈]0; 1[, λ? = 1 −

q f (c xN ) ?

?

xNλ = xc N

Internal tax λ does not depend on population’s size n ? → − x λ is a strong Nash equilibrium dλ?