request $500,000; then the Nash equilibrium response from management would be to also request $500,000. If management requests $500,000, then the Nash equilibrium response from workers would be to also request $500,000. Thus, the ($500,000, $500,000) payoff is also a Nash equilibrium. This game involves three Nash equilibriums out of nine possible solutions. In each Nash equilibrium, the entire profit-sharing pool is paid out. In the six remaining outcomes, some of the profit-sharing pool would not be distributed. Such suboptimal outcomes can and do occur in real-life situations.
However, in contemplating the bargaining process, workers are apt to note that a request for $0 is dominated by asking for either $500,000 or $1 million. If you do not ask for anything, you are sure of getting nothing. Similarly, management will never do worse, and may do better, if it asks for something. As a result, the $0 request strategy is dominated for both parties and will tend not to be followed. In addition, a request for the entire $1 million by either party will not be successful unless the other party requests nothing. Because a $0 request by either party is not likely, neither party is likely to request the full $1 million. In this case, the logical and rational request from each party is $500,000, or an equal 50/50 sharing of the profit pool.
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