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What Is True Halving in the Payoff Matrix of Game Theory?

Fig 2

Comparison between the utility criterion and quantitative criterion.

(a, b, c) The relationship between the gain and current wealth under the utility criterion (case 1, when u₁ = u₂ = 1). (d, e, f) The relationship between the utility and current wealth under the quantitative criterion (case 3). (a) The gain versus utility for both players, such that . Δg indicates the difference in g between the two players. (b) The difference in gain Δg (= |g₁ –g₂|) versus the difference in current wealth Δw (= |w₁ –w₂|). (c) Phase plane of Δg against w₁ and w₂. The dashed line indicate Δg = 0. (d) The utility versus both players’ gain, such that u_t = log{(g_t + w_t)/w_t}. Δu indicates the difference in u between the two players. (e) The difference in utility Δu (= |u₁ –u₂|) versus the difference in growth rate Δr (= r₁/r₂). (f) Phase plane of Δu versus w₁ and w₂. The dashed line indicates Δu = 0.

doi: https://doi.org/10.1371/journal.pone.0159670.g002