# Market Dynamics

There are several feedback mechanisms within the system. These are self-reinforcing behaviors; action 1 increases the rate of action 2 which increases the rate of action 1. Circular mechanics like thi

USD Sports Ecosystem is an innovation in the way people interact with sports markets. The motivation behind this essay is to delve deep into the USD Sports Markets, not from an operational or financial perspective, but with the purpose of analysing human interactions.

There are many fields that have something to say about human interaction but the field of study we will focus on here will be game theory - the study of strategic interdependence.

At its core this is an example of a prisoner's dilemma. A prisoner's dilemma is a situation where an individual's self interest is in conflict with a common goal, leading to the players within the game not cooperating despite it being in their best interests to cooperate.

In the case of currency, it is in each individual's best interest to use the most liquid, most widely used & stable currencies. The ‘common goal’ here is to remove reliance on centralized fiat currency and to maintain the individual's purchasing power. No individual acting alone can disentangle crypto from fiat; It takes mass coordination, along with alignment of incentives, and this is what USD Sports facilitates.

We will begin by outlining the essentials of game theory and analysing the prisoner's dilemma from a purely abstract perspective. We will then dive into the specific components of USD Sports Markets. We will take no shortcuts. USD Sports Markets is a complex Ecosystem that is the first of its kind and is deserving of deep and thorough analysis.

Game theory is the study of strategic interdependence. There are many situations in life where the best response to a situation depends on what other people in that situation do. Strategic situations are interesting because we can often get multiple outcomes, some of which are remarkably stable and yet sub-optimal for all people involved.

Consider a macroeconomic application of multiple stable outcomes under these conditions:

- Firms only invest if customers will buy goods.
- Customers only buy goods if they are paid wages.
- Customers are paid wages by firms only if they buy goods.

The optimistic (non-exhaustive) outcome:

- Firms think customers will buy goods and so expand production.
- Customers buy these goods because they think their wages are secure.
- The expanded profits allow firms to pay higher wages.

The pessimistic outcome:

- Firms do not think customers will buy goods and so restrict production to save costs.
- Customers restrict their purchasing because they lack wage security.
- Firms profits fall, leading to cost cutting in the form of wage cuts and layoffs.

We can see that no one wants to be in the pessimistic outcome and yet it is plausible. To understand why, we use game theory.

**Players**They make choices based on information they hold about themselves, the other players, and the structure of the game.

**Strategy**The full set of choices a player makes in a game.

**Payoffs**A payoff is the reward to each player, contingent upon the outcome of their interactions. We decide payoffs by considering each player's preferences within the game.

**Payoff Matrix**A table that lists all the available strategies and their respective payoffs.

Game theory is useful because it allows us to determine the optimal strategy which produces the best outcome for all the players involved.

The best way to get to grips with the power of game theory, is with an example.

The first game any student of game theory learns is the prisoner's dilemma. This is due to the fact that it is a simple game with applications to a wide variety of strategic situations. Once you see and understand it, you will see it at play everywhere.

The story goes like this. Two thieves plan to rob a store. As they approach the door, the police arrest them for trespassing. The police suspect that the pair planned to rob the store but they lack the evidence to prove it. They therefore, require a confession to charge the suspects with the more serious crime. The interrogator separates the suspects and tells them each:

*“We are charging you with trespassing which will land you in jail for a month. I know you were planning to rob the store but I cannot prove it without your testimony. Confess to me now, and I will dismiss your trespassing charge and set you free. Your friend will be charged for the attempted robbery and face 12 months in jail. I’m offering your friend the same deal. If you both confess, your individual testimony is no longer valuable and both of you will receive 8 months in jail.”*

Both players are self-interested and want to minimise their jail time. What should they do?

Using a payoff matrix allows us to condense all the information into an easy-to-analyse diagram:

Player 1’s available strategies are the rows (Quiet or Confess) and their corresponding payoffs are the first numbers in each cell.

Players 2’s available strategies are the columns and their corresponding payoffs are the second numbers in the cells.

If player 1 stays Quiet and player 2 stays Quiet the game ends in the top left corner of the matrix. If both players Confess the game ends in the bottom right corner of the matrix and so on.

To see which strategy each player will choose we should look at each move in isolation. From player 1’s perspective, what should he do if he thinks player 2 will stay Quiet?

We can see that player 1 should Confess because if he stays Quiet he will get one month in jail and we have already stated that both players prefer less time in jail.

What about if player 1 thought that player 2 was going to Confess?

Again it seems that player 1 should Confess as it leads to 8 months jail time rather than the 12 he will receive for keeping quiet.

Putting this together we reach an important conclusion:

**Player 1 is better off confessing regardless of player 2’s strategy.**Let’s look at player 2’s perspective, assuming he thinks player 1 will stay quiet:

Looking at the second numbers now we can see that like player 1, player 2 should confess as well: he will be set free instead of getting 1 month in jail.

Once again it looks like Confess should be the chosen strategy even if player 2 thinks player 1 will also Confess.

**Player 2 is also better off confessing regardless of player 1’s strategy.**

- We assumed that both players' preferences were to minimise their jail time
- We assumed both players were self-interested (i.e they don't care about their friends’ fate)
- We assumed only one interaction
- We assumed the players could not interact and plan their responses in advance

These assumptions led to a sub-optimal outcome in the game (Confess, Confess). We can see that had both players stayed quiet, they would have received less jail time. This is an

**unstable equilibrium**because –as we saw – both players are motivated to confess if they believe the other will stay quiet.Confess, Confess is therefore the only Nash equilibrium. A Nash equilibrium is a state in a game where no player wishes to deviate from their strategy, given what the other players are doing.

**If both players were able to cooperate with each other and stay Quiet however, they would have achieved a better outcome. This is an important conclusion as it shows us that two individuals may not cooperate, despite it appearing to be the best strategy for both.**

We can apply the model of the prisoner's dilemma to many real world situations. For example imagine the players being replaced with two countries. The strategies available to both countries are to arm themselves with weapons (replacing Confess) or disarm (replacing Quiet). In our first example the payoffs represented jail time. Payoffs do not actually have to represent a ‘real’ thing, they are really just the preferences and assumptions of the players captured in a number. What is important is that the payoffs have meaning relative to each other, and they remain consistent. So in our first game both players preferred lower scores. If we continue to assume that both players (countries) in this game want to minimise their score we get the following matrix:

Following the same steps as in the original game we can see that unfortunately (Arm, Arm) is the only dominant strategy. It is for this reason that efforts to unilaterally disarm are (in this author's opinion) doomed to fail. The specific payoffs chosen do not matter. What matters is that the relative differences between the payoffs fit our assumptions. Game theory cannot predict the future, it can only illustrate outcomes based on the preferences we set (via the payoffs chosen).