The Pokémon video games are largely based in strategy and relationships. To wit: the plots are almost always rooted in relationships – Ghetsis and N, Hilbert and N, Red and Giovanni, to name a few. Pokémon creatures and battling are the strategic aspects of the game. These two aspects of the game take up 90% of the game time, for example; completing the plot, creating competitive teams, completing the Pokédex. However, no game can function in a vacuum; these games need auxiliary functions to help propel them forwards and to ensure a coherent game.
One of these things that is not often given a second thought is the economic system in the video games. The animé has no monetary system to speak of, but the video games could not function without their ideologically nebulous economy. It is necessary for finishing the game and training a successful team – without money one could neither buy enough items to heal one's Pokémon at critical points nor buy enough items to strengthen and perfect the team. Ultimately, the economic system is a semi-utopian confluence of several existent economies.
In the video games, the player-character acquires money through battling, and the money earned is roughly proportional to the difficulty of the battle. Every trainer class has its own scaling (obviously Ladies and Rich Boys pay more at easier battles than do, say, Bug Catchers), but within that class, the pay scale increases with the difficulty of battle. This suggests some sort of merit-based system; the more successful one is at battling, the wealthier the person becomes. Nevertheless, almost every economic system is merit-based, from capitalism where the money one earns is based on the success of the product, to communism where the money earned is proportional to the contributions to society.
However, the defining characteristic of monetary acquisition is the positive feedback loop it creates – those who have money can train better Pokémon and win more money, and those without money cannot train their Pokémon and therefore are destined to poverty (which is where the “utopian” vision of the economics falls apart). The betterment of a Pokémon is highly dependent upon the amount of money spent – the more items used, the more likely that Pokémon will level up. If someone who has dozens of hyper potions battles someone who doesn't have any healing items at the same level, obviously the trainer with the money (as items cost money) will win the battle and make their Pokémon gain experience, and earn more money. This positive feedback loop feeds into the fact that an oligarchical structure exists – pointing to a capitalist society.
The “pure capitalism” hypothesis is only bolstered by the existence of the only sort of governing structure there is – the gym leaders and the Elite Four/Champion. Beating this upper echelon of trainers yields immense economic and social rewards. By running the gamut, you are accepted into their class, rewarded with the title of “champion.” This extreme upper class of Pokémon trainers is reminiscent of the intelligentsia of the 1920's – a few, wealthy, wildly successful businessmen that form a social clique, while the rest of the population suffers in content poverty (imagine a million Youngster Joeys). This rigidly-structured, almost caste-like system is quite comparable to the end result of a pure capitalism.
However, one puzzle piece is missing in the semi-utopian pure capitalism theory – the market. No oligarchy can stand if their lower class base is not purchasing anything. Which leaves one potential exit for the consumers' money – the Poké Marts. This integral portion of the economics does not appear to be capitalist at all – the prices of all the PokéMarts are standardized for the entire region, as are the items sold, by and large. Neither of these things fall under the aims of oligarchs – whose goal is to increase revenue. If they were to increase their revenue, they'd need to increase the prices gradually and introduce new products. Neither of these things have happened, and the fact that the price and selection of items has remained constant at the PokéMart suggests some form of communism, where a government standardizes the prices region-wide.
Other aspects of the game support the “communism” theory as well – the fact that the Pokémon Center offers what is essentially socialized medicine to Pokémon is one such aspect. Furthermore, the fact that there doesn't seem to be any sort of organized religion that dominates each region (there definitely is spirituality, however) also falls in line with the Communist ideal.
So the economy is not defined by either capitalism or communism, but some form of strange synthesis between those two. The fact that the video games are not centered around the economics makes this otherwise impossible system possible.