Expensive game

Two different ways to interpret “most expensive game”:

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Sold at auction

The record‐setting game in terms of sale price is Super Mario Bros. (1985, NES) — a sealed copy sold for about US $2 million. 
Another notable sale: a sealed copy of Super Mario 64 sold for about US $1.56 million. 
So if by “most expensive game” you mean “highest price paid for a collectible game copy,” the Mario one holds the record.

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Produced / Developed with highest budget

If instead you mean “which game cost the most to make / develop,” then the front‐runners are:
• Star Citizen — a still‐in‐development space sim, funded by crowdfunding & others; estimates of ~$777 million and rising. 
• Grand Theft Auto VI — still unreleased at this time, but reports suggest a budget of US $1 billion or more. 

So in that sense, Grand Theft Auto VI (once released) is expected to be the most expensive game ever developed.

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If you tell me which definition you meant (auction sale vs production/development cost) I can check the latest numbers for you.