2.1{a|=₁ ajzk} (a) ai where 1 is an indicator function, such that if total contributions exceed k units, then this term = 1, otherwise it is zero. a; is the level of contribution, where a¡ € {0,1}. u; (a) = Find the two Nash equilibria in this game and explain why these can be referred to as a Nash Equilibrium.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Help me understand this experiemental economics question 

Each of n players choose whether or not to contribute a fixed amount towards a public
good. The good is provided if and only if at least k people contribute, where 2 ≤ k < n; if
it is not provided, contributions are not refunded.
In other words, the preference of player i can be represented by the following utility
function:
u¡(a) = 2 · 1{a\[}}=₁ aj≥k} (a) ai
where 1 is an indicator function, such that if total contributions exceed k units, then this
term = 1, otherwise it is zero. a; is the level of contribution, where a¡ € {0,1}.
Find the two Nash equilibria in this game and explain why these can be referred to as a Nash
Equilibrium.
(Hint: Is there a Nash equilibrium in which more than k people contribute? One in which k
people contribute? One in which fewer than k people contribute? Do players have any
incentive to deviate given their contribution level?)
Transcribed Image Text:Each of n players choose whether or not to contribute a fixed amount towards a public good. The good is provided if and only if at least k people contribute, where 2 ≤ k < n; if it is not provided, contributions are not refunded. In other words, the preference of player i can be represented by the following utility function: u¡(a) = 2 · 1{a\[}}=₁ aj≥k} (a) ai where 1 is an indicator function, such that if total contributions exceed k units, then this term = 1, otherwise it is zero. a; is the level of contribution, where a¡ € {0,1}. Find the two Nash equilibria in this game and explain why these can be referred to as a Nash Equilibrium. (Hint: Is there a Nash equilibrium in which more than k people contribute? One in which k people contribute? One in which fewer than k people contribute? Do players have any incentive to deviate given their contribution level?)
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