25 February 2013 by Graham Morehead, posted in complex systems, economics, game theory

As mentioned last week, a U Maine economist named Sarah Morehead had this idea : Develop an economic environment in which selfish zero-sum-game strategies are maladaptive. (full disclosure: Sarah is my ex-wife)

You can file this idea under the headings, "Complex Adaptive Systems," and "Game Theory." This post merely presents these concepts and how they might work together. More meat will come in later posts.

Game Theory attempts to model interactions between people or other agents where each party has a choice or set of choices to make. Depending on circumstances, these choices may or may not be made with the knowledge of the other party's choices.

In a "zero-sum" game, the sum of the payoffs is always zero, i.e. any winnings I receive correspond directly to your losses; both players share a pie of fixed size. Oftentimes a zero sum is only true for the best outcomes, where others are worse than zero sum.

In real life, zero-sum games typically become worse-than-zero-sum due to the inefficiencies associated with payoff transfer. Consider the lottery. Its only function is to transfer wealth from the many to the few or the one (quite illogical, I know). The state takes a cut, and so do the ticket sellers. The winners share a pie that's smaller than what was lost by the losers -- worse than zero-sum.

The opposite of a zero-sum game would be a nonzero-sum game, which typically connotes a better than zero-sum interaction. Economics abounds with examples of this, and so does modern history. Bill Gates comes to mind. When Bill had to develop the first version of DOS, he bought the base of it from another programmer for a mere \$50K. In Bill's hands it was worth way more than that. To that programmer, however, he was probably receiving way more than the value he could have extracted from it. Both players won, and the ending value of both players payoffs was way more than \$50K. Next consider all of the money people and companies and people have paid to Microsoft during the PC revolution. To me it seems obvious that PC's brought computing to the common person and the common business. Of course I love Apple as well, but just consider how much value PC's have brought to companies in terms of productivity. I submit that people who purchased Microsoft products (during the 1990's especially), received more value than their price. These interactions were better than zero sum.

Sarah Morehead's idea considers the economy under the rubric of Complex Adaptive Systems, a special case of complex systems, where each agent is constantly adapting to the fitness landscape, which is itself constantly changing. For more background on this subject, see the many previous posts.

Game Theory often examines what strategies an agent should use. The word "strategy" can refer to a decision tree, i.e. a list of actions and responses to be used in a serial game. Strategies can be selfish and opportunistic, or they can be cooperative. Many theoretical exercises have shown what you and I already know -- cooperative is better. The immediate payoff is lower but the pie gets bigger. A good example is petty thievery. Whenever I go shopping for food, I always pay before leaving. Why? The apples have no RFID tags. No alarm is going to sound if I walk out with cheese in my pocket. Why doesn't everybody steal every day? We have all bought into the idea of cooperation, and rightly so! Since we trust each other and work together as a civilization, our stores are full of good food, and most people live in homes with clothing on their backs. If we all stole from each other on a consistent basis we would never have the world we now enjoy. Cooperation means we all take a smaller relative piece on any given day, but we still get more pie!

Those who cooperate gain a good reputation and have a good chance of finding others to cooperate with them. In a large anonymous society there are plenty of people who neither cooperate nor want to. However, they still receive cooperation from good trusting citizens like us. Such freeloaders can threaten systemic health if left unchecked.

The fear of freeloaders is rife in politically-charged discussions of healthcare and immigration. A lot of research has been done on the topic of punishing freeloaders. I think it's time we recognize that there are other solutions than punishment. People are smart. People are adaptive. Given the right conditions, people will cooperate.

more next time...

## 3 Responses to “Complex Adaptive Game Theory”

Fabulous blog! I might take issue with you in terms of the examples you have of 'better than zero sum' games. These are local gains, whereby two slices of the pizza make each other bigger, but does not the remaining pizza diminish accordingly? (Imagine two robbers sharing the loot from a heist - this is not the generation of wealth!). I'm no economist, but I often wonder if people don't confuse complexity of an economy with the concept of generation. Money (for example) is non-dissipative.
Anyhow, we should meet and eat pizza.
John