Book review: Game Theory

Authored by Laszló Mérő in 1998 (ISBN 0-387-98418-4).

Let's play the dollar auction.  It's like any other, with the winning bid handing over the bid and collecting the thing to be auctioned.  But there is this difference:  the runner-up also hands over its bid, but gets nothing in return.  I am auctioning a dollar.  Go!

The reader might think this is a simple game and that I, as the auctioneer, will be losing some money shortly.  According to author Mérő the average winning bid is $3.40!  I intend to try it at my first large gathering (one needs a critical mass of potential bidders for it to be effective).


This was such a fun book, but also a difficult read, requiring two passes for me to write intelligently about it.

There are four basic games, which I list below in order of my familiarity with them.

Chicken.  One variation has two cars speeding towards a cliff, the first car to turn away loses.  Another variation has two cars speeding towards each other, again the first car to turn away loses.  Here, close cooperation yields the best result, if both players agree to turn off at the same time.  Strong competition yields the worst result.  The best strategy, given the assumption that the players are not allowed to scheme together, is to appear as irrational and suicidal as possible.

Prisoner's dilemma.  Two players together commit and crime and speed away in separate cars.  Both are stopped for speeding and subsequently arrested for the crime.  Neither has positive or negative feelings for the other, the partnership designed to last only for the length of the crime.  The prosecutor approaches each, separately, the following proposition.
I do not have a strong case for the crime unless one or both of you confesses, though I have an easy case on the speeding.  If you confess to the crime and implicate your partner I will set you free and he will receive a ten year jail sentence.  If he confesses and you do not you will be sentenced to ten years and he will walk free.  If you confess and he does also then your testimony will be less valuable to me and I will not set either of you free and will instead seek (and receive) a five year sentence.  If neither of you confesses then I have no evidence on the crime and each of you will receive a one-year sentence for the speeding.
The possible outcomes are:

1. The players cooperate with each other by confessing, each spends five years in jail.
2. The players compete with each other by refusing to confess, each spends one year in jail.
3. One player cooperates and the other competes; the cooperating player spends 10 years in the jail and the other walks free.

In this game mutual competition yields the best result.

Gift of the Magi.  A couple is planning their evening.  They lay out their preferences but then need to leave for work.  They did not reach agreement, will have no opportunity to talk during the day, and must leave immediately after work to reach either option in time.  The options are these.  The husband prefers a sporting event, the wife a concert.  Both prefer most, however, spending the time together in either activity.  If each acts competitively and pursues their preferred activity they will not achieve the optimal outcome, spending time together; they will, however, somewhat enjoy the evening.  If each acts cooperatively and pursues the other's preferred activity they will again not achieve the optimal outcome and both will attend events neither enjoys.  The best outcome is achieved if one party acts competitively and the other cooperatively.

Holding the door.  Two people approach door.  They both most value passing through and they both also value holding the door for the other, allowing the other to pass first.  If each acts competitively by refusing to pass through the door before the other they achieve the worst outcome.  If each acts cooperatively then they achieve the best outcome.  If one acts competitively and one cooperatively then the competitor gets the best outcome and the cooperator gets an outcome with some positive value.

Returning to the dollar auction, a few months after writing the above I had a chance to play that game and another, the lowest-number game.  The lowest-number game is played as follows:  everyone writes on a piece of paper their name and a positive integer.  The player writing the lowest integer wins, with the exception that if two or more players select the same number then all such players are disqualified.

In the dollar auction the best I could do, with an audience of over 100, was to get bids of $1.01 and $1.00.  Perhaps my audience was especially intelligent.  I also played the lowest-number game with this audience.  The winning answer was 5.  Several players chose 1.  Sevens, and numbers ending in 7, were popular (7, 17, 27, 37, 1337, 11337, for example).  One player wrote 1.3 billion.

I really enjoy the lowest-number game because it can be played by anyone old enough to write his or her name.  Wisdom and experience do not seem to provide an edge, based on my observations of my children and their friends.  And, interesting patterns emerge when repeating play amongst the same players.  One eight-year-old consistently wrote "1" on her paper.  If you are competing against her, what is the best strategy?  Also write "1" preventing her from winning but also eliminating your own chances?  Never write "1", risking the situation where the other players follow suit?  Or, as the author states, employing a mixed strategy.  I suppose a mixed strategy in this case is writing "1" sometimes but not others and thus encouraging this player to select a different number

Book review: Alaska

Authored by Stephen Haycox in 2002 (ISBN 0-295-09249-7).  The subtitle is "An American Colony".

I knew from grade-school history that the United States purchased Alaska from Russia and that we got a good deal on the purchase (7 million dollars for more than 650,000 square miles).  I did not think about why we would purchase it or how it came to be owned by Russia in the first place.  America had not fully entered the industrial revolution at the time of the purchase in 1868 (or 1867, depending on whether one dates the purchase based on the agreement date or the settlement date).  Most people farmed and agriculture formed the backbone of economic activity.  Where enough people congregated into a small enough area, such as a city, one could make a living providing services.  This mass of people, however, was predicated on pre-existing agriculture.

In the Western states lack of water made agriculture difficult.  Frontiersmen sought gold and other natural resources.  Others followed to provide services.  After a location was played out the frontiersmen and the  population the supported them would move out.  Colorado today has 607 active cities or towns and 70 ghost towns, or more than one in nine.

Russia, and later the United States, viewed Alaska as a frontier, a place whose wealth could be exploited. The Natives (commonly referred to as Indians; both Alaska and the Western United States presented dozens of different groups) were a cheap source of labor and a pesky irritant unwilling to assimilate into the "superior" culture.  The Russians experienced the same cycle of aggression, trehostilities with Japan, the USSR emerged as a cold-war threat, aty, betrayal and back-and-force violence with the Natives that the United States experienced with the native populations in its West.  The Russians sold because the territory was more trouble than it was worth.  They never had more than a few hundred citizens or soldiers on the ground at any one time.  They constantly vied with the United States, Spain and Britain over control; they found it impossible to exert themselves over so much distance and over treacherous waters when the competing nations could crawl up-and-down the West coast.  While the Eastern-most point of Russia is only sixty miles across the Bering Straight to the Western-most point of Alaska, that point in Alaska is very far North and not so useful.  To trek from Russia to Alaska at a more temperate latitude is a 4,000-mile ocean voyage.

The agreement with Russia is perhaps not properly called a purchase.  Native Alaskans were living in Alaska well before the few hundred Russians arrived.  The late-arriving Russians could not properly be called owners.  Rather, the agreement was for the Russians to essentially quit and not resist.  William Seward, a former rival of Abraham Lincoln before becoming his Secretary of State, persuaded Congress on the investment.  While some in the press ridiculed the action as "Seward's Folly" most American supported the move, based on the wealth and resources available and the general sentiment that it was part of America's destiny to occupy North America.  After the purchase a military government was established.  What about statehood?

Statehood presented a chicken-and-egg problem.  The nation was not eager to extend statehood and the sharing that comes with it until the region was economically self-sufficient.  But the region had never been self-sufficient after the Russians disturbed the peace of the natives who had been living there.  Statehood and outside investment was needed, but who would make such investment given the uncertain contour of the rules that would apply?  Alaska made its way to statehood in two steps.

First, the discovery of gold in the late 1800s substantially increased the population.  As with other mineral rushes others joined the prospectors to provide services.  Salmon fishing and forestry provided employment, too.  The army built a telegraph line that connected Alaska with the mainland.  With the increased population, and inter-connection, Congress was willing to withdraw some national control in favor of local control:  towns could for the first time create some types of local government and appoint judges to handle local disputes.

Pearl Harbor accelerated the second step.  The United States was gripped with fear over Japanese intentions and capabilities.  Alaska, not far from the Japanese mainland, was unprepared, and the U.S. government started construction of military facilities there.  Indeed, Japan launched successful raids against two far-east Aleutian islands.  Ignominiously, Alaska was included with Western states in the roundup of citizens of Japanese descent and subsequent deportation to internment camps.  After World War II cooled and the cold-war heated, Alaska's location at the Eastern doorstep of the USSR further increased is military significance.  National dollars continued to flow in, resources continued to be extracted and settlers desired the self-governance and other amenities they had left at home.  Statehood passed the U.S. Congress in 1958 and Alaska officially entered the union in 1959.

The key decision upon statehood were the division of land and resources between Alaska, the United States and the native populations.  Most people recognized that the natives were here first and they were entitled to the land their houses sat on and that they farmed.  But, what of the mineral wealth underneath?  What of lands used by migrating animals that the natives used for subsistence?  What about lease payments that the state would be collecting on behalf of all Alaskans?  What about oil pipelines that would cross native lands?  Could native peoples refuse passage and, if not, what was a fair price for easements?

Prudhoe Bay, site of the United States' largest oil field, started producing oil in the late 1970s after completion of the Aleyska pipeline.  Alaska's share in this field yielded about 85 percent of its general revenue and in 1976 voters established the Alaska Permanent Fund as a place to store the excess.  Half of the earnings from this fund are distributed directly to citizens each year.  State government grew along with the state; oil prices and yield declined, but state spending did not.  Without a state income tax Alaska was soon in the red to the tune of one-half a billion dollars annually while, ironically, holding $27 billion in its permanent fund.  However, Alaska tends conservative and Republican and the population has little appetite for using the fund to fill the shortfall.  "Cut government" was the preferred,  and adopted, approach.

Alaska, like many Western states, is largely owned by the federal government.  Many Western residents resent that ownership; they conveniently forget that 100% of "their" land formerly belonged to the natives.  After the natives were pushed out 100% belonged to the federal government.  The fact that federal government granted ownership and use of some portion of that 100% should not cause one to complain about the remainder, as none has any right to any of it.

Few of the states are self-sufficient.  California is an exception, with agriculture and business interests that span human activity.  New York provides its own services but not its own food.  Midwestern states provide food but not services; they rely on coastal states for food markets.  Alaska is also not self-sufficient.  While food can be grown there the economies-of-scale enjoyed by Midwestern states causes food to be produced there and shipped; even the cost of shipping two thousand miles by rail and four thousand by ship does not enable Alaskans to compete for that market.  Statehood has given Alaska more, but not complete, control over absentee agricultural and energy investors.