By Ivan Uttley Game Theory (not to be confused with Gamification!) is a branch of Economics, and is a useful tool if used correctly. Economics, as a discipline, has had its detractors, and sometimes unfairly, for it is immature, and behavioural economics is making it more relevant again. Certainly, it is useful in understanding decision making and strategy, but don’t expect too much of it.
Some Concepts and Real Life Application The Spark! Power Hour sessions seek to apply these remedies
The Classic – Once off Prisoner’s Dilemma The Nash Equilibrium If A denies, but B confesses then B gets only 1 year in jail but A 10 years A Walks away free, B Walks away free A is Jailed for 6 months B is Jailed for 6 months This illustrates how an individually sub-optimal outcome is unavoidable when individuals seek to maximize their own gain or advantage or just protect themselves.
Repeated Games If two players play the prisoners' dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoners' dilemma. The iterated prisoners' dilemma game is fundamental to certain theories of human cooperation and trust. We assume rational Behaviour and that the game can model transactions between two people requiring varying levels of trust. There are many examples in human interaction and business as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to in economics, politics , sociology and evolutionary biology. Cooperative behaviour in populations or between businesses may be modelled by a multi-player, iterated, version of the game. Strategy here is aimed at two sets of tactics – what are they? How do you change the pay-offs to change the game dynamic? How do you signal to the other game participant? Collusion vs. Signalling? A better outcome can be gained by changing the pay-offs, and by communicating effectively.
Think of real life version of the Prisoner’s Dilemma Two scientists collaborating on a report would benefit if the other worked harder. But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project. Voluntary vaccination policies for childhood diseases present parents with a subtle challenge. If a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude complete eradication of a vaccine-preventable disease. Game theoretical analysis of this problem helps explain human decision-making with respect to vaccination. Increases in perceived vaccine risk will tend to induce larger declines in vaccine uptake for pathogens that cause more secondary infections (such as measles). After a vaccine scare, even if perceived vaccine risk is greatly reduced, it will be relatively difficult to restore pre-scare vaccine coverage levels. Consciously or not, we all play the prisoner’s dilemma from time to time
Use the game to understand the geo-political world • How has the Pakistan/India Pay-off Matrix emerged? Consider: • Both India and Pakistan develop nuclear fission devices, but no delivery capability. • Both sides obtain/develop a reliable delivery capability.. • How important is counter or secondary strike capability? • So when sharing a border and with only a few installations, what does the pay-off matrix look like today? • Show the Pay-Off Matrix that drove the Cold War Peace with respect to Nuclear Armament. • How important was it for the two sides to share information? How do you draw the pay-offs without the relevant information? The pay-off matrix between Russia & the US was fundamentally different than that which exists now between India and Pakistan. Escalation to include guarantees of mutual destruction by the US and Russia/China, perversely keep the peace….
Oligopolies What makes oligopolistic markets, which are characterized by a few large firms, so different from the other market structures we study in Microeconomics? Unlike in more competitive markets in which firms are of much smaller size and one firm’s behaviour has little or no effect on its competitors, an oligopolist that decides to lower its prices, change its output, expand into a new market, offer new services, or advertise, will have powerful and consequential effects on the profitability of its competitors. For this reason, firms in oligopolistic markets are always considering the behaviour of their competitors when making their business decisions. Is the SA Short-term Insurance Market an Oligopoly, what about Banking? How does commodity* pricing arise? In what kind of market? Is a Price war the outcome of intelligent business leaders making informed decisions? Will Price Wars always arise where there is no Collusion? * Commodity: The more specific meaning of the term commodity is applied to goods only. This class of goods has demand, in a market which is supplied without qualitative differentiation in the market A commodity has full or partial fungability i.e. the market treats its instances as equivalent or nearly so with no regard to who produced it
So why do banks in SA waste money on Advertizing? (people are more likely to get divorced than change their bank in SA!)
The Gender Battle A husband and wife are deciding whether to spend the evening at a Bullfight (Rugby) or the Opera (watching 7de Laan). The husband prefers the bullfight to the opera, but the wife prefers the opera to the bullfight. In this happy marriage (or jealous marriage), both would prefer to be together at either event rather than spending the evening apart. The worst outcome would be for the husband to spend the evening alone at the opera and the wife to spend the evening alone at the bullfight. Here we aim to capture issues where individuals wish to co-ordinate their actions but face a dispute as to what actions they should choose, similar to siblings choosing which game to play. *Note that the payoff numbers provided are arbitrary measures of misery/joy and only intended to illustrate the concept, not any actual result. ;-)
The Gender battle plays out in business for huge stakes! When played simultaneously, the Battle of the Sexes has two Nash equilibria: both choose Rugby or both choose 7de Laan. This is because if one spouse chooses Rugby or 7de Laan, then it is optimal for the other to choose the same because the couple would prefer to spend the evening together. The Battle of the Sexes/Gendres draws attention to the problem of co-ordination in games in which players have divergent preferences but a common interest in co-ordinating their strategies. In what consideration is this applicable in South Africa? An example corresponding to this game would be two firms competing over the adoption of an industry-wide standard for a product they have developed. The two firms would obviously have different preferences over the standard they would like the industry to adopt; however, both would like to co-ordinate on the same standard because consumers are more likely to buy a product with a common standard across the industry. Software standards are this game with pay-offs in the billions, hence the reason proprietary protocols exist in many industries. This is one instance where oligopolies can provide some benefit (there aren’t any others that come to mind)
The Sequential version of the Gender Game Consider the sequential version of the Battle of the Sexes in which the wife moves first, and the husband moves second after observing the action of the wife. The game tree for this game would be: 7de Laan Rugby 7de Laan Rugby 7de Laan Rugby How important is it to be certain of the pay-offs of the other player? Going first and moving on the WRONG pay-offs will be to the players disadvantage
The Sequential version of the Gender Game The sequential version of the Battle of the Sexes highlights an important principle First-mover advantage. The wife knows that the husband is rational and will always choose a best response to any action she chooses in the first stage. Therefore, she chooses Opera knowing that the husband's best response will be to choose Opera as well. Another co-ordinating mechanism is pre-play communication. If the husband and wife can discuss their strategies prior to deciding, they may argue a great deal, but they are likely to end up co-ordinating their choices or compromising. But how about changing future pay-offs? What if the husband chose the rugby anyway? This leads us to the concept of a Credible Threat – key to Game Theory and Parenting. The importance of a credible threat is key to the game – Tit 4 Tat is a winning strategy…..
A real world example Chicago's O'Hare International Airport is one of the world's busiest airports. Something had to be done to remove the congestion. Chicago Mayor, whose Chicago Airport Authority controlled the airport, was in favour of simply making necessary upgrades to the facilities at both O'Hare and Midway, Chicago's second airport. This was opposed by the Illinois governor and others, who favoured the idea of building a new airport south of the city – well outside the control of the Chicago Airport Authority. Mayor Daley made it clear on several occasions that he thought building a third airport was not only unnecessary, but also impossible because of the fact that no airlines seemed to be interested in the idea of flying in or out of another facility. Furthermore, because the new airport would not be in Chicago, the mayor announced that none of its funding would come from the city. Neither side was able to act without the other and they both knew it. One had political clout, whilst the other held veto power . A stalemate! It quickly became clear to both sides that if O'Hare continued to act as an international bottleneck, airlines would eventually find alternative routes. That outcome would have a deep and lasting effect on the Illinois economy. After years of mainly ignoring each other's opinions, meetings were held and it was suggested that there was enough room for both views to co-exist. Suddenly, there was talk of a third airport being built on a smaller scale in exchange for at least one new runway being built at O'Hare. This is how crises arise!
Moving first – always an advantage? We have seen in the gender game that if you have the pay-offs wrong, moving first is to your detriment. A situation many companies find themselves in where moving first may actually be a disadvantage is in research and development, and probably even more importantly, commercialisation of research and development. In those types of situations, the firm that moves first, if the technology is not patentable, goes to market with something. Then a second mover can actually observe the success or failure of the product and can come into the market quickly with a second generation product that can actually do better than the first generation product. In such situations, it is best to let your rival go first, commit to something in the market place, and then respond with what you have learnt. In other situations, going first may be an advantage, for example, building a plant with very large capacity or entering a market that may only have room for one firm. If you build a large store like Walmart has done in small markets, then going first is a great advantage because then you have got the assets in place. You are committed to be in that market and rivals will stay out. Therefore, the second mover in that situation never even shows up and will not enter the market. *Note that the payoff numbers provided in the examples below are arbitrary and only intended to illustrate the concept, not any actual result.
Game Theory Conclusions • Don’t use Game Theory as your primary strategy tool for ANY decision making, it is a tool that must be used with other tools. • Rather, use the game post-mortem points to check your thinking: • Have we got the pay-offs correct? • Will you ever get the pay-offs right, and does it matter? • How do you signal to your competitors without colluding? (and committing a crime) • Is your assumption of rational behaviour sound? • How do you avoid stupid and mindless price wars (sometimes they do serve a purpose!)