主题：【风言风雨】答阿康:囚徒两难和道德问题 -- 风雨声

中文说不清楚，俺用破英语解释一下，呵呵。不过关键之处是个人是效用最大化，而不是利益最大化。因为在模型中引入了善意和恶意两个变量，所以在构建utility function 时也应该加入这两个变量，后面会出现，在前面说一下。

Individuals maximise utilities instead of maximising profits, therefore, the payoff matrix should be showing individuals’ preference rather than profits outcome. We will see, later on, that under the different conditions there might exist different equilibriums, dominant strategy equilibrium (pareto optimum) or Nash equilibrium.

Assume individuals have homogenous preference (non-homogenous case would be more complicated), and the individuals’ utility function is U (profits, goodness, badness),simply, we suppose it’s the linear combination of U(profits)―utility of profits, U(goodness)―utility of choosing goodness, U(badness)―utility of choosing badness, i.e. U (profits, goodness, badness) = U(profits) + U(goodness) + U(badness). Based on observations of real world or common sense, we are able to assume that U (goodness) > 0, and U (badness) < 0), moreover, in order to have the payoff matrix as simple as possible, we let U (p) = p. Thus, the payoff matrix is

X

Goodness Badness

Goodness 100+U(G)/ 100+U(G) 150+U(B)/-200+U(G)

Y

Badness -200+U(G)/ 150+U(B) -50+U(B)/ -50+U(B)

The condition of choosing goodness is individual X’s dominant strategy is;

100+U(G) > 150+U(B) and -200+U(G) > -50+U(B)

.i.e. U(G) ?C U(B) > 150

same as Y’s

The condition of choosing badness is individual X’s dominant strategy is;

100+U(G) < 150+U(B) and -200+U(G) < -50+U(B)

.i.e. U(G) ?C U(B) < 150

same as Y’s

Thus, the condition for Goodness vs. Goodness being dominant strategy equilibrium is

U(G) ?C U(B) >150

And the condition for Badness vs. Badness being dominant strategy equilibrium is

U(G) ?C U(B) < 150

It’s clear that Badness vs. Badness is more likely to be dominant strategy equilibrium than Goodness vs. Goodness; however, Goodness vs. Goodness still has some chance to be dominant strategy equilibrium as well.

The condition for Goodness vs. Goodness being Nash equilibrium is

U(G) ?C U(B) >50

And the condition for Badness vs. Badness being Nash equilibrium is

U(G) ?C U(B) < 150

所以，出现那种equilibrium 取决于U(G)?CU(B)。当U(G)?CU(B)非常小,比如，小于50，即人们没有起码的道德底线，或不遵守道德底线的代价非常小，那么恶意对恶意占绝对上风，反之，如果U(G)?CU(B)非常大，比如大于150，即人们的道德水准非常高，常常以德服人或以德报怨，或不遵守道德底线的代价非常大，那么善意对善意会占绝对上风。如果U(G)?CU(B)适中，那么别人怎样对我，我就怎样对别人，就会占上风。根据统计学，我们知道第三种情况的例子占大多数，所以常看见的就是以牙还牙，以眼还眼，人敬一尺，我敬一丈的情况。

我觉得道德在经济活动中无足轻重，关键在于完备的regulation。好像跑题了，就这儿吧。呵呵