## Notes on the Economics of Game Theory - Part II

Written by Sam Vaknin

Games, naturally, can consist of one player, two players and more than two players (n-players). They can be zero (or fixed) - sum (the sum of benefits is fixed and whatever gains made by one of players are lost by others). They can be nonzero-sum (the amount of benefits to all players can increase or decrease). Games can be cooperative (where some of players or all of them form coalitions) – or non-cooperative (competitive). For some of games, solutions are called Nash equilibria. They are sets of strategies constructed so that an agent which adopts them (and, as a result, secures a certain outcome) will have no incentive to switch over to other strategies (given strategies of all other players). Nash equilibria (solutions) are most stable (it is where system "settles down", to borrow from Chaos Theory) – but they are not guaranteed to be most desirable. Consider famous "Prisoners' Dilemma" in which both players play rationally and reach Nash equilibrium only to discover that they could have done much better by collaborating (that is, by playing irrationally). Instead, they adopt "Paretto-dominated", or "Paretto-optimal", sub-optimal solution. Any outside interference with game (for instance, legislation) will be construed as creating a NEW game, not as pushing players to adopt a "Paretto-superior" solution.

The behaviour of players reveals to us their order of preferences. This is called "Preference Ordering" or "Revealed Preference Theory". Agents are faced with sets of possible states of world (=allocations of resources, to be more economically inclined). These are called "Bundles". In certain cases they can trade their bundles, swap them with others. The evidence of these swaps will inevitably reveal to us order of priorities of agent. All bundles that enjoy same ranking by a given agent – are this agent's "Indifference Sets". The construction of an Ordinal Utility Function is, thus, made simple. The indifference sets are numbered from 1 to n. These ordinals do not reveal INTENSITY or RELATIVE INTENSITY of a preference – merely its location in a list. However, techniques are available to transform ordinal utility function – into a cardinal one.

## The Distributive Justice of the Market - Part II

Written by Sam Vaknin

Philosophers tried to specify a "bundle" or "package" of goods, services, and intangibles (like information, or skills, or knowledge). Justice - though not necessarily happiness - is when everyone possesses an identical bundle. Happiness - though not necessarily justice - is when each one of us possesses a "bundle" which reflects his or her preferences, priorities, and predilections. None of us will be too happy with a standardized bundle, selected by a committee of philosophers - or bureaucrats, as was case under communism.

The market allows for exchange of goods and services between holders of identical bundles. If I seek books, but detest oranges - I can swap them with someone in return for his books. That way both of us are rendered better off than under strict egalitarian version.

Still, there is no guarantee that I will find my exact match - a person who is interested in swapping his books for my oranges. Illiquid, small, or imperfect markets thus inhibit scope of these exchanges. Additionally, exchange participants have to agree on an index: how many books for how many oranges? This is price of oranges in terms of books.

Money - obvious "index" - does not solve this problem, merely simplifies it and facilitates exchanges. It does not eliminate necessity to negotiate an "exchange rate". It does not prevent market failures. In other words: money is not an index. It is merely a medium of exchange and a store of value. The index - as expressed in terms of money - is underlying agreement regarding values of resources in terms of other resources (i.e., their relative values).

The market - and price mechanism - increase happiness and welfare by allowing people to alter composition of their bundles. The invisible hand is just and benevolent. But money is imperfect. The aforementioned Rawles demonstrated (1971), that we need to combine money with other measures in order to place a value on intangibles.

The prevailing market theories postulate that everyone has same resources at some initial point (the "starting gate"). It is up to them to deploy these endowments and, thus, to ravage or increase their wealth. While initial distribution is equal - end distribution depends on how wisely - or imprudently - initial distribution was used.

Egalitarian thinkers proposed to equate everyone's income in each time frame (e.g., annually). But identical incomes do not automatically yield same accrued wealth. The latter depends on how income is used - saved, invested, or squandered. Relative disparities of wealth are bound to emerge, regardless of nature of income distribution.

Some say that excess wealth should be confiscated and redistributed. Progressive taxation and welfare state aim to secure this outcome. Redistributive mechanisms reset "wealth clock" periodically (at end of every month, or fiscal year). In many countries, law dictates which portion of one's income must be saved and, by implication, how much can be consumed. This conflicts with basic rights like freedom to make economic choices.

The legalized expropriation of income (i.e., taxes) is morally dubious. Anti-tax movements have sprung all over world and their philosophy permeates ideology of political parties in many countries, not least USA. Taxes are punitive: they penalize enterprise, success, entrepreneurship, foresight, and risk assumption. Welfare, on other hand, rewards dependence and parasitism.

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