Blockchain gaming: single- or dual-token game economy?

--- tags: tokenomics --- # Blockchain gaming: single- or dual-token game economy? Following the tokenomics of Axie Infinity, many blockchain-based games, like Illuvium or Star Atlas, have chosen a dual-token model with a separation of the share token ([basket random](https://basketrandom.io)) and in-game currency (IGC). Thanks to the clear conceptual distinction between the gaming and investing functions, each token serves a well defined purpose. The IGC maintains a stable price by balancing the buying pressure exerted by new players entering the game with the selling pressure from existing players cashing out in-game rewards. The ST price increases with the growing number of players through the fees collected in the game. Despite the clear benefits of the dual-token model, some games (like Aurory or Defi Kingdom) have opted for a single-token model in which part of the ST supply is distributed to players as in-game incentives. Merging the two assets would expose the game to two opposite dangers: players with little wealth could be excluded from the game if the token becomes too expensive to acquire (lock-out risk). Conversely, in-game rewards could exert an inflationary pressure and prevent its price from increasing. The lock-out effect is best illustrated by the Ethereum native token \$ETH, which is both a utility token needed to insert transactions in the blockchain and a security token whose value increases with Ethereum usage. Yet, as the price of \$ETH increases, more and more users are excluded from the network. On the other hand, the single token model also presents some advantages. Distributing the main token as in-game rewards avoids the segregation of players and investor, and contributes to building a cohesive community. Moreover, the multiple uses of the main token strengthen its overall utility and market value. This note presents a simplified model of gaming economy with one or two tokens: an in-game currency (IGC) and/or a share token. We evaluate the capacity of each system to bring value to token holders on the premise that the game attracts a growing base of players. ## A game economy with in-game currency We set up a simplified economy composed of two assets: an IGC and an external asset which serves as numeraire (e.g. \$ETH or \$USDC). To access the game, players acquire $d_t$ units of the IGC at price $q_t$. One period later, they get $(1+r)d_t$ where $r$ is the reward from playing, then they sell at price $q_{t+1}$ and exit the game. The demand for IGC is inversely related to its price: $$ d_t = \dfrac{d}{q_t} $$ where $d>0$. The flow of new players $n_t$ is growing with time at a constant rate $g$: $n_t=(1+g)n_{t-1}$. The number of active players at each date is then: $x_t = n_t-n_{t-1}=gn_{t-1}$ which is also growing at rate $g$. The IGC price is determined by the demand-equal-supply equilibrium condition: $n_t d_t = n_{t-1} d_{t-1} (1+r)$ or $$ \dfrac{n_t d}{q_t} = \dfrac{n_{t-1} d (1+r)}{q_{t-1}} $$ On the left-hand side, the demand for IGC comes from new players entering the game, each buying $d_t$ units. On the right-hand side, the supply comes from players exiting the game and selling their $(1+r)d_{t-1}$ units. Therefore, the equilibrium market price growth rate is: $$ \dfrac{q_t}{q_{t-1}} =\dfrac{1+g}{1+r} $$ It means that the higher the price increase rate, the higher the user base growth rate $g$, and the smaller the rewards rate $r$ designed to incentivize the game. In this simple economy, a new IGC emitted at rate $r$ is not inflationary if it matches the economy's growth rate: $$ r=g $$  In-game rewards play an essential role in stabilizing the IGC price. Without them, it would increase over time making the game unaffordable for many users. At the same time, an excessively high rewards rate would lead to inflationary pressure and a downward trending price. An interesting property of this simple economy is that whatever the rewards rate $r$, the return from playing only depends on users' base growth rate: $$ \dfrac{(1+r)q_{t+1}}{q_t} = 1+g $$ Here the player buys one unit of resource at price $q_t$ and sells $1+r$ unit at price $q_{t+1}$ one period later. The higher the rewards rate, the higher the IGC inflation rate, which cancels the higher rewards off. ## Adding a share token It is possible to augment this simple economy by adding an ST. There is a treasury controlled by a DAO in which fees $y_t$ collected within the game are channelled to. Buy and sell operations in the marketplace are taxed at rate $\tau$: $$ y_t = \tau n_t q_t d_t = \tau n_t d $$ Fees growth rate is equal to the game's growth rate $g$. The return from playing is reduced by the fee rate: $$ (1+r)(1-\tau)\dfrac{q_{t+1}}{q_t} = (1+r)(1-\tau)\dfrac{1+g}{1+r} = (1-\tau)(1+g) $$ which means less demand for the IGC and less gaming activity. Contrary to the IGC, which has an uncapped supply, the ST has a fixed supply (equal to 1). Denoting by $p_t$ the ST price and applying the discounted cash flow pricing model: $$ p_t = \sum_{k=1}^{\infty} \dfrac{y_{t+k}}{(1+\rho)^k} = \sum_{k=1}^{\infty} \dfrac{y_t (1+g)^k}{(1+\rho)^k} = \dfrac{1+g}{\rho-g} \tau n_t d $$ with $\rho > g$ the discount rate. The ST price growth rate equals the game's growth rate $g$. We obtain a well-behaved dual-token economy with: - an IGC which price is stable insofar as the rewars rate tracks the game's growth rate - an ST which price captures the user base growth rate through a tax on trades ## A single-token economy A single-token economy is one in which the ST also serves as IGC. Its price is still determined by the discounted cash flow formula and the no-arbitrage condition. As in the two-token economy, if revenues generated by the protocol increase (decrease) beyond market expectations, higher (lower) return given to token-holders are arbitraged down (up) by a higher (lower) price. The fundamental difference is the absence of a second token which price balances supply and demand for in-game transactions. So, either demand for ST for in-game transactions is the short side of the market (and supply side is limited by the quantity demanded), or supply of ST is the short side (and demand is limited to the quantity supplied). Considering that the ST price grows at rate $g$ and the IGC price at rate (about) $g-r$ in the two-token economy, the most likely outcome is that demand for in-game trasanctions is driven down by high price and supply is constrained by demand. This is not to say that ST holders cannot exit the game by selling their tokens but that they prefer to stake them to earn the staking return. The financial motive of holding ST dominates the transaction motive. Fees are still a tax on in-game transactions: $$ y_t = \tau n_t p_t d_t = \tau n_t d $$ and fees growth rate is still equal to the game's growth rate $g$. We get the same cash-flow-based pricing formula: $$ p_t = \dfrac{1+g}{\rho-g} \tau n_t d $$ with $\rho > g$ the discount rate. The price growth rate is given by the players' growth rate $g$. The return from playing is now: $$ (1+r)\dfrac{p_{t+1}}{p_t} = (1+r)(1+g) $$ Game playing gives a double dividend: players get the reward $r$ and benefit from price appreciation $g$. At the same time, demand for in-game transactions is shrinking with price increase: $$ d_t = \dfrac{d}{p_t} $$ With a price increase rate equal to $g$, the demand decrease rate is (about) $-g$. This does not affect the volume of fees though, as the decreasing demand at rate $-g$ is compensated by an increasing price at rate $g$. The Table summarizes the differences between the two types of economy: | | Two tokens | One token | | ----------------------------- | :--------: | :-------: | | Players increase rate | $g$ | $g$ | | ST price increase rate | $g$ | $g$ | | IGC price increase rate | $g-r$ | $-$ | | Return to play | $g$ | $g+r$ | | Transaction demand per player growth rate| $r-g$ | $-g$ | To sum up, a single token economy has only an ST, which price increases with the number of players. This drives out demand for in-game transactions on the intensive margin (the average transaction per player), but not on the extensive margin (players are still willing to buy some ST to play ot to earn the staking return rate). When those two effects are combined, game's profitability is not impaired as fees are collected on decreasing transaction volume but increasing transaction price. This also makes the game more financially attractive for players as they buy a token which appreciates over time. Overall, I find that the single-token economy brings as much value to token-holders as a two-token economy and strengthens gaming incentives by sharing game's upside potential with players.